"Given the values for sin t and cos..." was answered by our experts

High School
Geometry
Trigonometry
Trigonometric Functions

alesterp

Answered question

2021-03-06

Given the values for sin t and cos t, use reciprocal and quotient identities to find the values of the other trigonometric functions of t.

\sin t = \frac{3}{4} and \cos t = \frac{\sqrt{7}}{4}

Answer & Explanation

BleabyinfibiaG

Skilled2021-03-07Added 118 answers

Consider the given trigonometric function sint and cost.
The other trigonometric functions values are find as,
Use the trigonometric formula,
$\tan t = \frac{\sin t}{\cos t}$
$\csc t = \frac{1}{\sin t}$
$\sec t = \frac{1}{\cos t}$
$\cot t = \frac{\cos t}{\sin t}$
Now, substitute the given trigonometric function values in the above formula,
Since $\sin t = \frac{3}{4} and \cos t = \frac{\sqrt{7}}{4}$
Thus, $\tan t = \frac{\sin t}{\cos t} = \frac{\frac{3}{4}}{\frac{\sqrt{7}}{4}} = \frac{3}{\sqrt{7}}$
$\csc t = \frac{1}{\sin t} = \frac{1}{\frac{3}{4}} = \frac{4}{3}$
$\sec t = \frac{1}{\cos t} = \frac{1}{\sqrt{\frac{3}{4}}} = \frac{4}{\sqrt{7}}$
$\cot t = \frac{\cos t}{\sin t} = \frac{\frac{\sqrt{7}}{4}}{\frac{3}{4}} = \frac{\sqrt{7}}{3}$

Jeffrey Jordon

Expert2021-12-14Added 2605 answers

Answer is given below (on video)

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