Question

question 3
use a graphing calculator to evaluate. round to 3 decimal places.
cos (260°) =

question 4
use a graphing calculator to evaluate. round to 3 decimal places.
sec (162°) =

question 5
use reference angles to evaluate the expression.
tan (240°) =

Explanation:

Question 3

Step1: Use calculator

Input $\cos(260^{\circ})$ in a graphing calculator.

Step2: Round to 3 decimal places

$\cos(260^{\circ})\approx - 0.174$

Question 4

Step1: Use reciprocal identity

Since $\sec\theta=\frac{1}{\cos\theta}$, then $\sec(162^{\circ})=\frac{1}{\cos(162^{\circ})}$

Step2: Calculate with calculator

Input $\cos(162^{\circ})$ in calculator, then take its reciprocal. $\cos(162^{\circ})\approx - 0.951$, so $\sec(162^{\circ})=\frac{1}{\cos(162^{\circ})}\approx - 1.052$

Question 5

Step1: Find reference angle

For $\theta = 240^{\circ}$, the reference angle $\theta_{r}=240^{\circ}-180^{\circ} = 60^{\circ}$

Step2: Determine sign

Since $240^{\circ}$ is in the third - quadrant, and $\tan\theta$ is positive in the third - quadrant.

Step3: Evaluate using reference angle

$\tan(240^{\circ})=\tan(60^{\circ})=\sqrt{3}\approx1.732$

Answer:

Question 3: $-0.174$
Question 4: $-1.052$
Question 5: $1.732$