Find the values of the trigonometric functions sine and sec of θ with the given constraint.
Function Value
Constra int
Tan θ = - sin θ 0

A)sin θ = - sec θ =
B)sin θ = sec θ = -
C)sin θ = sec θ = -
D)sin θ = sec θ =
E)sin θ = - sec θ = -

Question

Find the values of the trigonometric functions sine and sec of θ with the given constraint. ​
Function Value
Constra int
Tan θ = -  sin θ > 0
​​
A)sin θ = - sec θ = 
B)sin θ = sec θ = - 
C)sin θ = sec θ = - 
D)sin θ = sec θ = 
E)sin θ = - sec θ = -

Quizplus · Accepted Answer

We know that tan θ = -11, and since sin θ is positive, we can assume that θ lies in the second quadrant, where sine is positive and tangent is negative. Using the Pythagorean identity, we have:

sin^2 θ + cos^2 θ = 1

sin^2 θ + (-11)^2 = 1

sin^2 θ = 122/122 = 1

sin θ = ±1

Since we know that sin θ is positive, we have:

sin θ = 1

cos θ = -1/11 (using the definition of tangent)

sec θ = 1/cos θ = -11

Therefore, the correct answer is B.

Find the Values of the Trigonometric Functions Sine and Sec