Answer

Verified

447.9k+ views

Hint: Here we are given angle $\theta =-30{}^\circ $ and we have to find the value of $\cos \theta $ . So for that substitute the value of $\theta =-30{}^\circ $ in $\cos \theta $. Try it, you will get the answer.

Complete step-by-step answer:

The trigonometric functions (also called circular functions, angle functions, or trigonometric functions) are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena, through Fourier analysis.

The most widely used trigonometric functions are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used in modern mathematics.

The cosine function, along with sine and tangent, is one of the three most common trigonometric functions. In any right triangle, the cosine of an angle is the length of the adjacent side (A) divided by the length of the hypotenuse (H). In a formula, it is written simply as '$\cos $'. $\cos $ function (or cosine function) in a triangle is the ratio of the adjacent side to that of the hypotenuse. The cosine function is one of the three main primary trigonometric functions and it is itself the complement of sine (cos + sine).

The cosine graph or the cos graph is an up-down graph just like the sine graph. The only difference between the sine graph and the cos graph is that the sine graph starts from $0$ while the cos graph starts from $90{}^\circ $ (or $\dfrac{\pi }{2}$).

We are given angle $\theta =-30{}^\circ $ .

So now we have to find $\cos \theta $ .

Let us substitute the value $\theta =-30{}^\circ $ in $\cos \theta $, we get,

\[\cos \theta =\cos (-30{}^\circ )\]

We know that, $\cos (-a)=\cos a$.

\[\cos \theta =\cos (-30{}^\circ )=\cos 30{}^\circ =\dfrac{\sqrt{3}}{2}\]

Here, we get the value of $\cos \theta $ at $\theta =-30{}^\circ $ is $\dfrac{\sqrt{3}}{2}$ .

Note: Read the question carefully. Do not make silly mistakes. Don’t get confused while solving the problem. Your concept regarding trigonometric functions should be clear. Do not jumble yourself while simplifying.

Complete step-by-step answer:

The trigonometric functions (also called circular functions, angle functions, or trigonometric functions) are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena, through Fourier analysis.

The most widely used trigonometric functions are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used in modern mathematics.

The cosine function, along with sine and tangent, is one of the three most common trigonometric functions. In any right triangle, the cosine of an angle is the length of the adjacent side (A) divided by the length of the hypotenuse (H). In a formula, it is written simply as '$\cos $'. $\cos $ function (or cosine function) in a triangle is the ratio of the adjacent side to that of the hypotenuse. The cosine function is one of the three main primary trigonometric functions and it is itself the complement of sine (cos + sine).

The cosine graph or the cos graph is an up-down graph just like the sine graph. The only difference between the sine graph and the cos graph is that the sine graph starts from $0$ while the cos graph starts from $90{}^\circ $ (or $\dfrac{\pi }{2}$).

We are given angle $\theta =-30{}^\circ $ .

So now we have to find $\cos \theta $ .

Let us substitute the value $\theta =-30{}^\circ $ in $\cos \theta $, we get,

\[\cos \theta =\cos (-30{}^\circ )\]

We know that, $\cos (-a)=\cos a$.

\[\cos \theta =\cos (-30{}^\circ )=\cos 30{}^\circ =\dfrac{\sqrt{3}}{2}\]

Here, we get the value of $\cos \theta $ at $\theta =-30{}^\circ $ is $\dfrac{\sqrt{3}}{2}$ .

Note: Read the question carefully. Do not make silly mistakes. Don’t get confused while solving the problem. Your concept regarding trigonometric functions should be clear. Do not jumble yourself while simplifying.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How many crores make 10 million class 7 maths CBSE

The 3 + 3 times 3 3 + 3 What is the right answer and class 8 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE