Question

The point (−3, 1) is on the terminal side of angle Θ, in standard position. What are the values of sine, cosine, and tangent of Θ? Make sure to show all work. (10 points)

Answer 1

The angle is in the second quadrant  so only the sine is positive . 
Length of the hypotenuse = sqrt (-1^2 + 3^2)  = sqrt10
sine  =  1/sqrt10 =  0.3162 to 4 dec places
tangent = 1 / -3 =  -0.3333  to 4 d p's
cosine = -3/sqrt10 = -0.9487 to 4 d, p's.

Answer 2

To solve this problem yo need to have the "x", the "y", and the radius. To find the radius since it is not given we use the formula.

sq rt(-3^2+1^2)

sq rt(9+1)

sq rt(10) would be the length of the radius in this case.

Then we use the sine cosine and tangent fractions

sin:y/r

cos:x/r

tan:y/x

With the values plugged in the equations are

SIN:1/sqrt(10) Since there can´t be a sq rt in hte denominator we change it to 1(sq rt(10))/10

COS:-3/sqrt(10) Since there can´t be a sq rt in the denominator we change it to -3(sq rt(10))/10

TAN:1/-3 This one can stay the same.

This would be the measures of SIN, COS, and TAN.