Question

for help with question 1, refer to example 1.

1. use a scientific calculator to find each value to four decimal places.

a) sin 42° b) sin 33° c) cos 19°
d) sin 88° e) cos 74° f) cos 38°
g) sin 45° h) cos 42°

1. use a scientific calculator to find the measure of each angle a to the nearest degree.

a) sin a = 0.6092 b) cos a = 0.4067 c) sin a = 0.1425
d) sin a = 0.7777 e) cos a = 0.3907 f) sin a = 0.2861
g) cos a = 0.5736 h) cos a = 0.7193

Explanation:

Step1: Use scientific - calculator for sine and cosine values

Use a scientific calculator to find the sine and cosine of the given angles and round to four decimal places.

Step2: Use inverse - trigonometric functions for angle measures

Use the inverse - sine (sin⁻¹) and inverse - cosine (cos⁻¹) functions on the scientific calculator to find the angle measures and round to the nearest degree.

1.

a) $\sin42^{\circ}\approx0.6691$
b) $\sin33^{\circ}\approx0.5446$
c) $\cos19^{\circ}\approx0.9455$
d) $\sin88^{\circ}\approx0.9994$
e) $\cos74^{\circ}\approx0.2756$
f) $\cos38^{\circ}\approx0.7880$
g) $\sin45^{\circ}\approx0.7071$
h) $\cos42^{\circ}\approx0.7431$

2.

a) $A = \sin^{-1}(0.6092)\approx38^{\circ}$
b) $A=\cos^{-1}(0.4067)\approx66^{\circ}$
c) $A = \sin^{-1}(0.1425)\approx8^{\circ}$
d) $A=\sin^{-1}(0.7777)\approx51^{\circ}$
e) $A=\cos^{-1}(0.3907)\approx67^{\circ}$
f) $A=\sin^{-1}(0.2861)\approx17^{\circ}$
g) $A=\cos^{-1}(0.5736)\approx55^{\circ}$
h) $A=\cos^{-1}(0.7193)\approx44^{\circ}$

Answer:

Step1: Use scientific - calculator for sine and cosine values

Use a scientific calculator to find the sine and cosine of the given angles and round to four decimal places.

Step2: Use inverse - trigonometric functions for angle measures

Use the inverse - sine (sin⁻¹) and inverse - cosine (cos⁻¹) functions on the scientific calculator to find the angle measures and round to the nearest degree.

1.

a) $\sin42^{\circ}\approx0.6691$
b) $\sin33^{\circ}\approx0.5446$
c) $\cos19^{\circ}\approx0.9455$
d) $\sin88^{\circ}\approx0.9994$
e) $\cos74^{\circ}\approx0.2756$
f) $\cos38^{\circ}\approx0.7880$
g) $\sin45^{\circ}\approx0.7071$
h) $\cos42^{\circ}\approx0.7431$

2.

a) $A = \sin^{-1}(0.6092)\approx38^{\circ}$
b) $A=\cos^{-1}(0.4067)\approx66^{\circ}$
c) $A = \sin^{-1}(0.1425)\approx8^{\circ}$
d) $A=\sin^{-1}(0.7777)\approx51^{\circ}$
e) $A=\cos^{-1}(0.3907)\approx67^{\circ}$
f) $A=\sin^{-1}(0.2861)\approx17^{\circ}$
g) $A=\cos^{-1}(0.5736)\approx55^{\circ}$
h) $A=\cos^{-1}(0.7193)\approx44^{\circ}$