Question

use the trigonometric function values of the quadrantal angles to evaluate the given expression.
7(sec 0°)² + 7(cot 270°)² + csc 90°

7(sec 0°)² + 7(cot 270°)² + csc 90° =
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall trig - values of quadrantal angles

We know that $\sec0^{\circ}=\frac{1}{\cos0^{\circ}} = 1$, $\cot270^{\circ}=\frac{\cos270^{\circ}}{\sin270^{\circ}}=0$, and $\csc90^{\circ}=\frac{1}{\sin90^{\circ}} = 1$.

Step2: Substitute the values into the expression

Substitute $\sec0^{\circ}=1$, $\cot270^{\circ}=0$, and $\csc90^{\circ}=1$ into $7(\sec0^{\circ})^2 + 7(\cot270^{\circ})^2+\csc90^{\circ}$. We get $7\times(1)^2+7\times(0)^2 + 1$.

Step3: Simplify the expression

First, calculate $7\times(1)^2=7$, $7\times(0)^2 = 0$. Then $7 + 0+1=8$.

Answer:

$8$