Question

solve the following using your calculator. (7 pts each)
round to 4 decimal places.
round to the nearest whole degree.
\\( \sin 35 ^ { \circ } = \\)
\\( \sin a = \frac { 7 } { 12 } \\)
\\( m \angle a = \\)
\\( \cos 49 ^ { \circ } = \\)
\\( \cos a = \frac { 8 } { 17 } \\)
\\( m \angle a = \\)
\\( \tan 36 ^ { \circ } = \\)
\\( \tan a = \frac { 8 } { 3 } \\)
\\( m \angle a = \\)

Explanation:

Step1: Calculate sine, cosine, tangent values

• For $\sin35^{\circ}$, using a calculator, $\sin35^{\circ}\approx0.5736$
• For $\cos49^{\circ}$, using a calculator, $\cos49^{\circ}\approx0.6561$
• For $\tan36^{\circ}$, using a calculator, $\tan36^{\circ}\approx0.7265$

Step2: Calculate angles from trigonometric ratios

• If $\sin A=\frac{7}{12}$, then $A = \sin^{-1}(\frac{7}{12})\approx35^{\circ}$ (using calculator's inverse - sine function)
• If $\cos A=\frac{8}{17}$, then $A=\cos^{-1}(\frac{8}{17})\approx62^{\circ}$ (using calculator's inverse - cosine function)
• If $\tan A=\frac{8}{3}$, then $A=\tan^{-1}(\frac{8}{3})\approx69^{\circ}$ (using calculator's inverse - tangent function)

Answer:

$\sin35^{\circ}\approx0.5736$, $\cos49^{\circ}\approx0.6561$, $\tan36^{\circ}\approx0.7265$, $m\angle A\approx35^{\circ}$ (when $\sin A = \frac{7}{12}$), $m\angle A\approx62^{\circ}$ (when $\cos A=\frac{8}{17}$), $m\angle A\approx69^{\circ}$ (when $\tan A=\frac{8}{3}$)