
What are the six trigonometric function values of 540?
Answer
442.8k+ views
Hint: To find the six trig function values of 540, we need to draw the unit circle first. The angle is given in degree so convert it into radian. Now, so and will lie on the X' axis. The values of sine and cosine on X’ axis are given by point . Now, using these two values we can find the remaining 4 trig function values easily.
Complete step by step solution:
In this question, we have to find the six trigonometric function values of 540.
The six trigonometric functions are sin, cos, tan, cosec, sec and cot.
Now, the angle is given in degrees in our question. We have to convert it in radian first of all.
So, to convert degree into radian, we multiply degree with .
Therefore, .Now, let us draw a unit circle to find these trig function values.
Now, we need to find .
1)
All the points on the unit circle are represented by
lies on the X' axis and the coordinates at X’ axis are .
Hence, the value of all on X’ axis will be equal to 0.
Hence, .
Therefore, .
2)
lies on the X' axis and the coordinates at X’ axis are .
Hence, the value of all on X’ axis will be equal to .
Hence, .
Therefore, .
3)
We know that , and we have the values of and .
Therefore,
4)
We know that cosec is the inverse of sine. So, we can write as .
And
not defined.
5)
We know that sec is the inverse of cos. So, we can write as .
And
6)
We know that cot is the inverse of tan. So, we can write as .
And .
not defined
Hence, we have found all the six trig function values of 540.
Note: In first quadrant , all the values of trig functions are positive.
In second quadrant , the values of only sine and cosecant are positive
In third quadrant , the values of only tangent and cotangent are positive.
In fourth quadrant , the values of only cosine and secant are positive.
Complete step by step solution:
In this question, we have to find the six trigonometric function values of 540.
The six trigonometric functions are sin, cos, tan, cosec, sec and cot.
Now, the angle is given in degrees in our question. We have to convert it in radian first of all.
So, to convert degree into radian, we multiply degree with
Therefore,

Now, we need to find
1)
All the points on the unit circle are represented by
Hence, the value of all
Hence,
Therefore,
2)
Hence, the value of all
Hence,
Therefore,
3)
We know that
Therefore,
4)
We know that cosec is the inverse of sine. So, we can write
And
5)
We know that sec is the inverse of cos. So, we can write
And
6)
We know that cot is the inverse of tan. So, we can write
And
Hence, we have found all the six trig function values of 540.
Note: In first quadrant
In second quadrant
In third quadrant
In fourth quadrant
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