5.08 Using radians
Calculate the following trigonometric ratios to two decimal places:
\sin \dfrac{35 \pi}{16}
\cos 6.87
\sin 7.26
\tan 7.26
\tan \left(\dfrac{- 3 \pi}{7}\right)
\cos \dfrac{2 \pi}{3}
\sin \left( - \dfrac{4 \pi}{3}\right)
Consider the following diagram:
Find the length of side h.
Hence, state the exact value of:
Consider the following diagram:
Find the length of the hypotenuse, h.
Hence, state the exact value of:
Consider the unit circle diagram and state the exact value of the following trigonometric ratios:
\sin \dfrac{\pi}{2}
\cos \dfrac{3\pi}{2}
\tan \pi
\cos 0
\sin \left(-2\pi\right)
Find the exact value of the following:
\sin \dfrac{\pi}{3} + \cos \dfrac{\pi}{3}
\sin \dfrac{\pi}{6} \cos \dfrac{\pi}{4}
\dfrac{\sin \frac{\pi}{3}}{\cos \frac{\pi}{6}}
\sin \dfrac{\pi}{4} \cos \dfrac{\pi}{6} + \tan \dfrac{\pi}{4}
\sin ^{2}\left(\dfrac{\pi}{6}\right) - \cos ^{2}\left(\dfrac{\pi}{3}\right)
2\sin ^{2}\left(\dfrac{\pi}{2}\right) + 3\cos ^{2}\left(\dfrac{\pi}{2}\right)
Consider the unit circle shown, where points A and B have the same \\ y-coordinates.
Suppose that \theta = \dfrac{10 \pi}{11}. State the size of the reference angle, \alpha.
Consider the unit circle shown, where the line through A and B passes through the origin, O.
Suppose that \theta = \dfrac{8 \pi}{7}. State the size of the reference angle, \alpha.
Consider the unit circle shown, where the points A and B have the same \\ x-coordinate.
Suppose that \theta = \dfrac{9 \pi}{5}. State the size of the reference angle, \alpha.
Find the exact value of the following:
\sin \dfrac{5 \pi}{6}
\tan \dfrac{3 \pi}{4}
\sin \dfrac{7 \pi}{6}
\cos \dfrac{7 \pi}{6}
\sin \dfrac{5 \pi}{3}
\cos \dfrac{5 \pi}{3}
\cos 4 \pi
\tan 9 \pi
\sin \dfrac{ 5\pi}{2}
\cos \dfrac{ 7\pi}{2}
\cos \dfrac{3 \pi}{4}
\tan \dfrac{7 \pi}{6}
\tan \dfrac{11 \pi}{6}
Find the exact value of the following:
\sin \left( - \dfrac{17 \pi}{6} \right)
\cos \left( - \dfrac{17 \pi}{6} \right)
\cos \left( - \dfrac{4 \pi}{3} \right)
\tan \left( - \dfrac{17 \pi}{6} \right)
Find the exact value of the following:
\dfrac{\left(\sin \dfrac{2 \pi}{3}\right) \left(\cos \dfrac{2 \pi}{3}\right) \left(\tan \dfrac{3 \pi}{4}\right)}{\tan \left( - \dfrac{\pi}{4} \right)}
\dfrac{\sin \dfrac{2 \pi}{3} + \cos \dfrac{5 \pi}{6} - \tan \dfrac{7 \pi}{4}}{\cos \dfrac{4 \pi}{3}}
Consider the equation y = \sin x.
Complete the table with values in exact form:
| x | 0 | \dfrac{\pi}{6} | \dfrac{\pi}{2} | \dfrac{5 \pi}{6} | \pi | \dfrac{7 \pi}{6} | \dfrac{3 \pi}{2} | \dfrac{11 \pi}{6} | 2 \pi |
|---|---|---|---|---|---|---|---|---|---|
| \sin x |
Sketch a graph for y = \sin x on the domain -2\pi \leq 0 \leq 2\pi.
State the value of \sin \left(-2 \pi\right).
State the sign of \sin \left( \dfrac{- \pi}{12} \right).
State the sign of \sin \dfrac{13 \pi}{12}.
Which quadrant of a unit circle does an angle with measure \dfrac{13 \pi}{12} lie in?
Consider the equation y = \cos x.
Complete the table with values in exact form:
| x | 0 | \dfrac{\pi}{3} | \dfrac{\pi}{2} | \dfrac{2 \pi}{3} | \pi | \dfrac{4 \pi}{3} | \dfrac{3 \pi}{2} | \dfrac{5 \pi}{3} | 2 \pi |
|---|---|---|---|---|---|---|---|---|---|
| \cos x |
Sketch a graph for y = \cos x on the domain -2\pi \leq 0 \leq 2\pi.
State the value of \cos \pi.
State the sign of \cos \left( \dfrac{- \pi}{4} \right).
State the sign of \cos \dfrac{11 \pi}{6}.
Which quadrant of a unit circle does an angle with measure \dfrac{11 \pi}{6} lie in?
Consider the equation y = \tan x.
Complete the table with values in exact form:
| x | 0 | \dfrac{\pi}{4} | \dfrac{\pi}{2} | \dfrac{3 \pi}{4} | \pi | \dfrac{5 \pi}{4} | \dfrac{3 \pi}{2} | \dfrac{7 \pi}{4} | 2 \pi |
|---|---|---|---|---|---|---|---|---|---|
| \tan x |
Sketch the graph of y = \tan x on the domain -2\pi \leq 0 \leq 2\pi.
Graph the line y = 1 on the same coordinate plane.
Hence, state the exact solutions to the equation \tan x = 1 over this domain.
State the value of \tan \left(-2 \pi\right).
State the sign of \tan \left( \dfrac{- \pi}{6} \right).
State the sign of \tan \dfrac{9 \pi}{5}.
Which quadrant of a unit circle does an angle with measure \dfrac{9 \pi}{5} lie in?
Consider the function y = 5 \sin x.
Sketch the graph of the given function over the domain \left[ - 2 \pi , 2 \pi\right].
Graph the line y = x on the same coordinate plane.
Hence, state the number of solutions to the equation 5 \sin x = x.
Consider the graph of y = - \tan x and the plotted points A, B, C, D and E shown:
At which point is the graph of \\ y = -\tan x equal to zero?