For what values of θ is cosθ>−sinθ when π/2≤θ<3π/2

Step-by-step explanation:

Given the inequality cosθ>−sinθ, to get the value of that falls within the range π/2≤θ<3π/2, the following steps must be followed;

Step 1;

Divide both sides by cosθ;

cosθ/cosθ>−sinθ/cosθ

1>−sinθ/cosθ

1>-tanθ

Step 2;

Multiplying both sides by -1

-1<tanθ

tanθ>-1

θ>

θ>-45°

Since tan is negative in the second and 4th quadrant;

In the second quadrant θ>180-45

θ>135°

θ>3π/4

in the 4th quadrant, θ>360-45

θ>315°

θ>9π/4

The only value that falls within the range is at when θ>3π/4  

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step-by-step explanation:

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