7.03 Periodicity
Determine whether the following ratios will have positive or negative answers:
\sin 143 \degree
\tan 284 \degree
\cos 143 \degree
\cos 284 \degree
\sin 284 \degree
\cos 269 \degree
\sin 170 \degree
\cos 320 \degree
Determine whether the following statements are true or false:
\sin 70 \degree is positive.
\sin 110 \degree is negative.
\sin 250 \degree is negative.
\sin 290 \degree is negative.
For each of the following trigonometric expressions:
State the quadrant where the angle is found.
Find the value of the related positive acute angle.
Is the expression positive or negative?
Rewrite the expression in terms of its relative acute angle.
\sin 135 \degree
\tan 120 \degree
\cos 240 \degree
Rewrite the following trigonometric expressions in terms of their relative acute angle:
\sin 106 \degree
\cos 149 \degree
\tan 124 \degree
\cos 579 \degree
\tan 465 \degree
\sin 240 \degree
\cos 315 \degree
\tan 140 \degree
\tan 380 \degree
\sin 174 \degree
\cos 210 \degree
\tan 295 \degree
\tan \left( - 70 \degree \right)
\sin \left( - 50 \degree \right)
\cos \left( - 80 \degree \right)
\cos \left( - 110 \degree \right)
For each of the following expressions, find the equivalent trigonometric expression in the first quadrant:
Using the approximations \cos 21 \degree = 0.93 and \sin 21 \degree = 0.36, find the approximate value of the following trigonometric expressions, correct to two decimal places:
\cos 159 \degree
\sin \left( - 159 \degree \right)
Determine whether the following expressions are equal to \sin \left(360 \degree + \theta\right):
Determine whether the following expressions are equal to \cos \theta:
\cos \left(360 \degree - \theta\right)
\sin \left(180 \degree - \theta\right)
- \cos \left(180 \degree + \theta\right)
\sin \left(90 \degree - \theta\right)
Simplify the following:
\sin \left(180 \degree - \theta\right)
\cos \left(360 \degree - \theta\right)
\sin \left( - \theta \right)
Consider the following trigonometric expressions:
Find the value of the related acute angle.
Hence, find the exact value of the trigonometric expression.
\cos \left( - 135 \degree \right)
\cos \left( - 120 \degree \right)
Find the exact value of the following trigonometric expressions:
\sin 315 \degree
\cos 315 \degree
\tan 315 \degree
\sin 855 \degree
\cos 855 \degree
\tan 855 \degree
\sin (-135) \degree
\cos (-225) \degree
\tan 135 \degree
\sin 240 \degree
\cos 300 \degree
\tan 405 \degree