Trigonometry ratio. Evaluate the following and show your workings. A.cos 222° B.sin 212° c.sin 242° D.sin190° E.tan 310° F.cos 283° G.sin 320° H.cos 350 °
A. cos 222° = -0.766
Using a calculator, we can find the cosine of 222 degrees to be approximately -0.766.
B. sin 212° = -0.208
Using a calculator, we can find the sine of 212 degrees to be approximately -0.208.
C. sin 242° = -0.939
Using a calculator, we can find the sine of 242 degrees to be approximately -0.939.
D. sin 190° = -0.342
Using a calculator, we can find the sine of 190 degrees to be approximately -0.342.
E. tan 310° = -0.648
Using a calculator, we can find the tangent of 310 degrees to be approximately -0.648.
F. cos 283° = -0.935
Using a calculator, we can find the cosine of 283 degrees to be approximately -0.935.
G. sin 320° = 0.342
Using a calculator, we can find the sine of 320 degrees to be approximately 0.342.
H. cos 350° = 0.939
Using a calculator, we can find the cosine of 350 degrees to be approximately 0.939.
A. cos 222°:
To evaluate cos 222°, we can use the fact that cos (180° + θ) = -cos θ.
So, cos 222° = -cos (180° + 42°).
Now, we know that cos 42°.
Therefore, cos 222° = -cos 42°.
B. sin 212°:
To evaluate sin 212°, we can use the fact that sin (180° + θ) = -sin θ.
So, sin 212° = -sin (180° + 32°).
Now, we know that sin 32°.
Therefore, sin 212° = -sin 32°.
C. sin 242°:
To evaluate sin 242°, we can use the fact that sin (180° + θ) = -sin θ.
So, sin 242° = -sin (180° + 62°).
Now, we know that sin 62°.
Therefore, sin 242° = -sin 62°.
D. sin 190°:
To evaluate sin 190°, we can use the fact that sin (180° + θ) = -sin θ.
So, sin 190° = -sin (180° + 10°).
Now, we know that sin 10°.
Therefore, sin 190° = -sin 10°.
E. tan 310°:
To evaluate tan 310°, we can use the fact that tan (180° + θ) = tan θ.
So, tan 310° = tan (180° + 130°).
Now, we know that tan 130°.
Therefore, tan 310° = tan 130°.
F. cos 283°:
To evaluate cos 283°, we can use the fact that cos (360° - θ) = cos θ.
So, cos 283° = cos (360° - 77°).
Now, we know that cos 77°.
Therefore, cos 283° = cos 77°.
G. sin 320°:
To evaluate sin 320°, we can use the fact that sin (360° - θ) = sin θ.
So, sin 320° = sin (360° - 40°).
Now, we know that sin 40°.
Therefore, sin 320° = sin 40°.
H. cos 350°:
To evaluate cos 350°, we can use the fact that cos (360° - θ) = cos θ.
So, cos 350° = cos (360° - 10°).
Now, we know that cos 10°.
Therefore, cos 350° = cos 10°.