Question

A point P (x, y) is shown on the unit circle U corresponding to a real number t. Find the values of the trigonometric functions at t.

Answer 1

sin(t)=8/17
cos(t)=-15/17
tan(t)=-8/15
sec(t)=-17/15
csc(t)=17/8
cot(t)=-15/8

Answer 2

Point P is on the unit circle U. The values of trigonometric functions at t are $sin\theta=\dfrac{8}{17},\;cos\theta=-\dfrac{15}{17}$$,tan\theta=-\dfrac{8}{15},\;cot \theta=-\dfrac{15}{8},\;cosec\theta=\dfrac{17}{8},\;sec\theta=-\dfrac{17}{15}$.

Given:

From the given figure, the coordinate of point P is $(-\dfrac{15}{17}, \dfrac{8}{17})$.

The point P is present on a unit circle U. So, in general, the coordinates of a point on the circle will be $(x,y)\equiv (cos\theta, sin\theta)$.

By comparing the given coordinate with the general expression, the value sine and cosine function will be,

$sin\theta=\dfrac{8}{17}\\cos\theta=-\dfrac{15}{17}$

Now, the other trigonometric functions will be,

$tan\theta=\dfrac{sin\theta}{cos\theta}\\tan\theta=-\dfrac{8}{15}\\cot \theta=-\dfrac{15}{8}\\cosec\theta=1/sin\theta=\dfrac{17}{8}\\sec\theta=1/cos\theta=-\dfrac{17}{15}$

Therefore, the values of trigonometric functions at t are $sin\theta=\dfrac{8}{17},\;cos\theta=-\dfrac{15}{17}$$,tan\theta=-\dfrac{8}{15},\;cot \theta=-\dfrac{15}{8},\;cosec\theta=\dfrac{17}{8},\;sec\theta=-\dfrac{17}{15}$.

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