Trigonometric Ratios of Any Angle?

Question

I have to determine the exact values of sin, cos, and tan for: P(8,15) From that I have my x and y values (8,15) and then I figured out my r value which is 17. Then I put sin as 15/17, cos as 8/17 and tan as 15/8. When I looked in the back of the book it said cos was 8/15. Anyone know why they did that?

Answer 1

SOH-CAH-TOA.

Right triangle:
Opposite side = 15
Adjacent side = 8
Hypotenuse = 17 (sqrt(8² + 15²) = 17)

So
sin(angle) = O/H = 15/17
cos(angle) = A/H = 8/17
tan(angle) = O/A = 15/8

I agree with you and think the book has it wrong...

Another confirmation:
tan(angle) should equal sin(angle) / cos(angle).
tan(angle) = 15/17 divided by 8/17
tan(angle) = 15/8

So cos(angle) should definitely be 8/17... must be a typo.

The only explanation is that perhaps it was the cotangent? cot(angle) = 1/tan(angle) = 8/15...

Answer 2

Sounds like a typo to me. Wouldn't be the first time I've seen an error in a textbook.