Question

question 6
fill in the following with the exact value of the trig. ratios using the given angle:
θ = -90°
sinθ =
cosθ =
tanθ =
secθ =
cscθ =
cotθ =

Explanation:

Step1: Convert angle to positive coterminal

$-90^\circ + 360^\circ = 270^\circ$ (coterminal angle)

Step2: Find $\sin(-90^\circ)$

$\sin(-90^\circ) = -\sin(90^\circ) = -1$

Step3: Find $\cos(-90^\circ)$

$\cos(-90^\circ) = \cos(90^\circ) = 0$

Step4: Find $\tan(-90^\circ)$

$\tan\theta = \frac{\sin\theta}{\cos\theta} = \frac{-1}{0}$ (undefined)

Step5: Find $\sec(-90^\circ)$

$\sec\theta = \frac{1}{\cos\theta} = \frac{1}{0}$ (undefined)

Step6: Find $\csc(-90^\circ)$

$\csc\theta = \frac{1}{\sin\theta} = \frac{1}{-1} = -1$

Step7: Find $\cot(-90^\circ)$

$\cot\theta = \frac{\cos\theta}{\sin\theta} = \frac{0}{-1} = 0$

Answer:

$\sin\theta = -1$, $\cos\theta = 0$, $\tan\theta$ undefined, $\sec\theta$ undefined, $\csc\theta = -1$, $\cot\theta = 0$