The terminal point P(θ) lies on the line segment joining (0,0) and (8, 15) Draw a sketch and find the values of the circular functions on `(0,pi/2)`Show complete solution and explain the answer.
(1) Draw a right triangle in the first quadrant with vertices A(0,0),B(8,15), and C(8,0). Angle `theta` is `/_BAC` .
(2) The six circular functions are sin,cos,tan,sec,csc,cot. To find the values recall that:
`cos theta = "adj"/"hyp"`
`tan theta = "opp"/"adj"`
with csc the reciprocal of the sin, sec the reciprocal of the cos, and cot the reciprocal of the tan.
** opp is the side opposite `theta` which is `bar(BC)` , adj is the side adjacent to `theta` which is `bar(AC)` , and hyp is the hypotenuse or `bar(AB)`
(3) Using the pythagorean theorem (or recognizing the pythagorean triplet) we know that `AC=8,BC=15,AB=17`
`sin theta =15/17 ` `cos theta=8/17` `tan theta = 15/8`
`csc theta = 17/15` `sec theta = 17/8` `cot theta = 8/15`