Let θ be an angle in quadrant 2 such that cotθ = -3/8. Find the exact values of sinθ and secθ

Question

Let θ be an angle in quadrant 2 such that cotθ = -3/8.

Find the exact values of sinθ and secθ

sinθ =

secθ =

Answer 1

Let θ be an angle in quadrant 2 such that cotθ = -3/8. Find the exact values of sinθ and secθ

Let θ be an angle in quadrant 2 such that cotθ = -3/8.

Find the exact values of sinθ and secθ

sinθ =

secθ =

Hello Tetro,

First, I suggest you construct the triangle on a x,y-coordinate system. Using cotθ = -3/8.

Because cotθ = cosθ / sinθ, this infers the x-coordinate or the cos is -3 ( it gets the - sign because the x's are negative in the 2^nd quadrant) and the y-ccordinate, or the sin is 8.

...........y-axis

\...........¦ 8

..\.........¦

....\.......¦

......\ ....¦

........\ ..¦

........θ\ ¦

———————— x-axis

-3

With the adjacent side of the triangle = -3 , and the opposite side = 8, determine the hypotenuse using the pythagorean theorem.

a² + b² = c²

(-3)² + (8)² = c²

9 + 64 = c²

c = √73

Secondly, with the opp, adj, and hyp sides of the triangle known, find the exact values of sinθ and secθ:

sinθ = opp / hyp

sinθ = 8 / √73 or with a rationalized denominator: sinθ = 8√73 / 73

secθ = hyp / adj

secθ = √73 / -3

Answer 2

Please see video.