Question

trig ratios/finding angles practice
2 of 4
solve for x to the nearest thousandths.
$\tan x = 0.4663$
$cos x \approx 0.8956$
$cos x \approx 0.5150$
$sin x \approx 0.2356$
$sin x \approx 0.7431$
$\tan x \approx 12.6542$
$\boldsymbol{85.482^\circ}$ $\boldsymbol{13.627^\circ}$ $\boldsymbol{59.003^\circ}$ $\boldsymbol{47.996^\circ}$

Explanation:

Step1: Solve $\tan x=0.4663$

$x = \arctan(0.4663) \approx 25.000^\circ$

Step2: Solve $\cos x=0.8956$

$x = \arccos(0.8956) \approx 26.414^\circ$

Step3: Solve $\cos x=0.5150$

$x = \arccos(0.5150) \approx 59.003^\circ$

Step4: Solve $\sin x=0.2356$

$x = \arcsin(0.2356) \approx 13.627^\circ$

Step5: Solve $\sin x=0.7431$

$x = \arcsin(0.7431) \approx 47.996^\circ$

Step6: Solve $\tan x=12.6542$

$x = \arctan(12.6542) \approx 85.482^\circ$

Answer:

$\cos x \approx 0.5150$ matches $59.003^\circ$
$\sin x \approx 0.2356$ matches $13.627^\circ$
$\sin x \approx 0.7431$ matches $47.996^\circ$
$\tan x \approx 12.6542$ matches $85.482^\circ$

Filled pairs:
$25.000^\circ$ $\tan x = 0.4663$
$59.003^\circ$ $\cos x \approx 0.5150$
$47.996^\circ$ $\sin x \approx 0.7431$
$26.414^\circ$ $\cos x \approx 0.8956$
$13.627^\circ$ $\sin x \approx 0.2356$
$85.482^\circ$ $\tan x \approx 12.6542$