Sin Cos Tan Values Table Formulas and Solved Examples for All Angles
The concept of sin cos tan values plays a key role in mathematics and is widely applicable in both real-life situations and competitive exam questions. Whether you're preparing for school exams, JEE, or just want to solve trigonometry problems faster, knowing these values and how to remember them is essential.
What Are Sin Cos Tan Values?
Sin cos tan values are the standard results of the basic trigonometric ratios — sine (sin), cosine (cos), and tangent (tan) — at commonly used angles such as 0°, 30°, 45°, 60°, and 90°. These values connect angles with sides of right-angled triangles and are used to solve height, distance, and other practical problems in Maths, Physics, and Engineering.
Key Formula for Sin Cos Tan
Here are the standard formulas that define these ratios in any right-angled triangle with an angle \( θ \):
- sin θ = Opposite Side / Hypotenuse
- cos θ = Adjacent Side / Hypotenuse
- tan θ = Opposite Side / Adjacent Side
Sin Cos Tan Values Table (0°, 30°, 45°, 60°, 90°)
Learn and use these sin, cos, tan values for quick reference during exams and problem solving. This printable chart is a must-memorize for all students.
| Angle (θ) | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | ∞ |
Sin Cos Tan Values in Radians
Many exams and higher studies use radians instead of degrees. Here are the same values in radians:
| Angle (θ) | 0 | π/6 | π/4 | π/3 | π/2 |
|---|---|---|---|---|---|
| sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | ∞ |
Memory Trick: Sin Cos Tan Hand Rule
A simple way to remember the sin cos tan table is to use your left hand. For angles (0°, 30°, 45°, 60°, 90°), fold the finger that matches the angle (starting from the thumb as 0°). The number of fingers on the left = sin value; fingers on the right = cos value. Divide by 2 and take the square root as needed. The SOHCAHTOA rule is also useful: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
When to Use Sin, Cos, or Tan?
Use sin when you know or need the opposite and hypotenuse, cos for adjacent and hypotenuse, and tan for opposite and adjacent sides. These ratios help in solving triangles, heights and distances, and even engineering design problems. Students preparing for competitive exams like JEE and NEET can save a lot of time by instantly recalling these values.
Solved Example with Sin Cos Tan Values
Let's look at a typical exam question using these values:
Example: In triangle ABC, right-angled at B, with AB = 24 cm and BC = 7 cm, find sin A and cos A.
1. Use Pythagoras: AC² = AB² + BC² = 24² + 7² = 576 + 49 = 625
2. So, AC = 25
3. sin A = Opposite/Hypotenuse = BC/AC = 7/25
4. cos A = Adjacent/Hypotenuse = AB/AC = 24/25
Practice Questions: Check Your Sin Cos Tan Skills
- What is sin 60°?
- Find tan 45° using the value table.
- If cos A = 1/2, what is the angle A?
- Use the hand trick to find sin 30°.
- Calculate cos (90° – θ) if sin θ = 1/2.
Frequent Errors and Misunderstandings
- Swapping sine and cosine values for the same angle.
- Forgetting to rationalize denominators for tan/cot values.
- Applying the wrong ratio (using sin when adjacent side is needed).
Relation to Other Trigonometry Topics
Knowing sin cos tan values makes it easier to tackle trigonometric ratios, trignometric values table, and apply concepts in real-world applications. Once memorized, these values help solve tougher problems like identities, equations, and inverse trig functions.
We explored sin cos tan values — including key formulas, value tables, memory hacks, and solved examples. With continuous practice and smart tricks, you'll become fast and accurate in using these ratios in any trigonometry problem. For more guidance and expert tips, visit Vedantu’s Trigonometric Functions or attend a live session. Keep practicing!
Also Read: Trigonometric Ratios | SOHCAHTOA Explained | Trigonometric Functions
FAQs on Sin Cos Tan Values and Trigonometric Ratios Explained
1. What are sin, cos, and tan in trigonometry?
The trigonometric ratios sin, cos, and tan relate the angles of a right triangle to the ratios of its sides. In a right-angled triangle:
- sin θ = opposite / hypotenuse
- cos θ = adjacent / hypotenuse
- tan θ = opposite / adjacent
2. What are the standard sin, cos, and tan values for 0°, 30°, 45°, 60°, and 90°?
The standard trigonometric values for special angles are fixed and widely used in problem solving.
- sin 0° = 0, cos 0° = 1, tan 0° = 0
- sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3
- sin 45° = 1/√2, cos 45° = 1/√2, tan 45° = 1
- sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3
- sin 90° = 1, cos 90° = 0, tan 90° = not defined
3. How do you find sin, cos, and tan of an angle in a right triangle?
To find sin θ, cos θ, and tan θ, identify the sides relative to angle θ and apply the basic trigonometric ratios.
- Step 1: Identify opposite, adjacent, and hypotenuse.
- Step 2: Use formulas:
• sin θ = opposite / hypotenuse
• cos θ = adjacent / hypotenuse
• tan θ = opposite / adjacent
4. Why is tan 90° not defined?
The value of tan 90° is not defined because it involves division by zero. Since tan θ = sin θ / cos θ and cos 90° = 0, we get tan 90° = 1/0, which is undefined in mathematics. Division by zero has no real value, so tan 90° does not exist.
5. What is the relationship between sin, cos, and tan?
The primary relationship between sin, cos, and tan is given by the identity tan θ = sin θ / cos θ. Another important identity is:
- sin²θ + cos²θ = 1
6. How do you remember sin, cos, and tan formulas easily?
You can remember the sin, cos, and tan formulas using the mnemonic SOH-CAH-TOA.
- SOH: sin = opposite / hypotenuse
- CAH: cos = adjacent / hypotenuse
- TOA: tan = opposite / adjacent
7. What is the difference between sine and cosine?
The difference between sine and cosine lies in the sides they compare in a right triangle. sin θ compares the opposite side to the hypotenuse, while cos θ compares the adjacent side to the hypotenuse.
- sin θ = opposite / hypotenuse
- cos θ = adjacent / hypotenuse
8. How do you calculate tan from sin and cos?
You calculate tangent using the identity tan θ = sin θ / cos θ. For example, if sin θ = 1/2 and cos θ = √3/2, then:
- tan θ = (1/2) ÷ (√3/2)
- = 1/√3
9. In which quadrants are sin, cos, and tan positive?
The signs of sin, cos, and tan depend on the quadrant of the angle.
- 1st quadrant: sin, cos, tan are all positive
- 2nd quadrant: only sin is positive
- 3rd quadrant: only tan is positive
- 4th quadrant: only cos is positive
10. What are some real-life applications of sin, cos, and tan?
The trigonometric functions sin, cos, and tan are used to measure heights, distances, and angles in real life. Common applications include:
- Finding the height of buildings or trees using tan θ
- Calculating wave motion and sound frequencies using sin and cos
- Engineering and construction angle measurements
- Navigation and GPS calculations
