Question

Assume the given point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle: (-2, 10).

Answer 1

first, plot the point and draw a line from (0,0) to the point. can you do that ?

Answer 2

@phi Ok I did it.

Answer 3

next, we form a triangle by dropping a line straight down until it hits the x-axis

label the sides: x is -2, y is +10
you need the length of the hypotenuse. can you find it ?

Answer 4

I think so.
The length of the legs are 10 and 2
The hypotenuse squared equals the sum of both legs squared. So...
10^2+2^2=104
sqrt104=10.2
So the hypotenuse equals 10.2

Right?

Answer 5

@phi

Answer 6

yes, but if you want exact numbers, use \( \sqrt{104} = 2 \sqrt{26} \)

now form ratios for sin, cos, tan, and their reciprocals c s c , sec , cot

Answer 7

notice the question asks for *the exact values*, so we can't use the rounded decimal value for the sqrt(104)

Answer 8

use SOH CAH TOA or oscar had a heap of apples to remember the ratios for sin, cos, and tan

Answer 9

How do I form ratios? :/

Answer 10

By definition, the angle is


to find the sin, cos, etc, we use the *reference angle*