Consider the equilateral triangle with side lengths of 2 \text{ cm}.
Find the exact values of the following:
Perpendicular height of the triangle.
Size of angle x.
\sin 60 \degree
\cos 60 \degree
\tan 60 \degree
\sin x
\cos x
\tan x
Consider the right-angled triangle where \angle ABC measures 45 \degree and AC = 1 unit. Find the exact value of the following:
Length of BC.
Exact length of AB.
\sin 45 \degree
\cos 45 \degree
\tan 45 \degree
Find the exact side length of an equilateral triangle with a perpendicular height of \sqrt{21} \text{ cm}.
Consider the following diagram of the unit circle:
Find the exact value of the following:
\cos \dfrac{\pi}{3}
\sin \dfrac{\pi}{3}
\sin \dfrac{\pi}{4}
\cos \dfrac{\pi}{6}
\cos \dfrac{\pi}{2}
\sin \dfrac{\pi}{2}
\cos 2\pi
\tan \dfrac{\pi}{6}
Find the exact value of the following:
\cos 0 \degree
\sin 90 \degree
\tan 90 \degree
\tan 30 \degree.
\sin 30 \degree
\cos 30 \degree
\sin 45 \degree
\tan 45 \degree
Evaluate the following, leaving your answers in exact form:
\dfrac{\sin 30 \degree}{\cos 60 \degree}
\sin 45 \degree + \cos 60 \degree
\sin \dfrac{\pi}{6} \cos \dfrac{\pi}{4}
\sin 45 \degree \cos 30 \degree + \tan 45 \degree
\cos^{2}\left(30 \degree\right)
\cos^{2}\left(\dfrac{\pi}{4}\right)
\sin ^{2}\left(\dfrac{\pi}{6}\right) - \cos ^{2}\left(\dfrac{\pi}{3}\right)
\sin ^{2}\left(30 \degree\right) + \cos ^{2}\left(30 \degree\right)
Prove the following equations are true:
\tan 30 \degree \times \cos 30 \degree = \cos 60 \degree.
\tan \dfrac{\pi}{3} \times \cos \dfrac{\pi}{6} =\tan \dfrac{\pi}{4}
Find the values of the following:
\cos 720 \degree
\sin 630 \degree
\tan \left( - 630 \degree \right)
\cos \left( - 180 \degree \right)
\sin \dfrac{5\pi}{2}
\cos 5\pi
\tan \dfrac{7\pi}{2}
\cos \left(-\dfrac{5\pi}{2}\right)
The first diagram shows a unit circle with point P \left(\dfrac{1}{\sqrt2}, \dfrac{1}{\sqrt2}\right) marked on the circle. Point P represents a rotation of 45 \degree anticlockwise around the origin from the positive x-axis:
Find the exact values of the following:
\sin 45\degree
\cos 45\degree
\tan 45\degree
On the second diagram, the coordinate axes shows a 45 \degree angle that has also been marked in the second, third, and fourth quadrants. For each of the following quadrants, find the relative angle:
Quadrant 2
Quadrant 3
Quadrant 4
The points Q, R and S mark rotations of point P to the corresponding angles on the unit circle. State the exact coordinates of each point:
Q
R
S
Write the following in terms of an equivalent ratio of 45 \degree:
\sin 135\degree
\cos 225 \degree
\tan 315 \degree
\sin \left(-45 \right) \degree
Hence find the exact value of the following:
\sin 135\degree
\cos 225 \degree
\tan 315 \degree
\sin \left(-45 \right) \degree
The first diagram shows a unit circle with point P \left(\dfrac{1}{2}, \dfrac{\sqrt{3}}{2}\right) marked on the circle. Point P represents a rotation of 60 \degree anticlockwise around the origin from the positive x-axis:
Find the exact values of the following:
\sin 60\degree
\cos 60\degree
\tan 60\degree
On the second diagram, the coordinate axes shows a 60 \degree angle that has also been marked in the second, third, and fourth quadrants. For each quadrant, find the relative angle.
Quadrant 2
Quadrant 3
Quadrant 4
The points Q, R and S mark rotations of point P to the corresponding angles on the unit circle. State the exact coordinates of each point:
Q
R
S
Write the following in terms of an equivalent ratio of 60 \degree:
\sin 120\degree
\cos 240 \degree
\tan 300 \degree
\cos \left(-60 \right) \degree
Hence find the exact value of the following:
\sin 120\degree
\cos 240 \degree
\tan 300 \degree
\cos \left(-60 \right) \degree
The first diagram shows a unit circle with point P \left(\dfrac{\sqrt{3}}{2}, \dfrac{1}{2}\right) marked on the circle. Point P represents a rotation of 30 \degree anticlockwise around the origin from the positive x-axis:
Find the exact values of the following:
\sin 30\degree
\cos 30\degree
\tan 30\degree
On the second diagram, the coordinate axes shows a 30 \degree angle that has also been marked in the second, third and fourth quadrants. For each quadrant, find the relative angle:
Quadrant 2
Quadrant 3
Quadrant 4
The points Q, R and S mark rotations of point P to the corresponding angles on the unit circle. State the exact coordinates of each point:
Q
R
S
Write the following in terms of an equivalent ratio of 30 \degree:
\cos 150\degree
\sin 210 \degree
\tan 330 \degree
\cos \left(-30 \right) \degree
Hence find the exact value of the following:
\cos 150\degree
\sin 210 \degree
\tan 330\degree
\cos \left(-30 \right) \degree
Find the exact values of the following:
\sin \left(\dfrac{7 \pi}{6}\right)
\cos \left(\dfrac{2 \pi}{3}\right)
\tan \left(\dfrac{7 \pi}{4}\right)
\sin \left(\dfrac{19 \pi}{6}\right)
\cos \left( - \dfrac{\pi}{6} \right)
\tan \left(\dfrac{11 \pi}{4}\right)
\tan \left(-\dfrac{ \pi}{6}\right)
\sin \left(-\dfrac{5 \pi}{6}\right)
Find the exact values of the following:
\sin \dfrac{\pi}{2}
\tan \dfrac{3 \pi}{2}
\sin \dfrac{5 \pi}{6}
\tan \dfrac{3 \pi}{4}
\sin \dfrac{7 \pi}{6}
\tan \dfrac{7 \pi}{6}
\cos \dfrac{5 \pi}{3}
\sin \left( - \dfrac{\pi}{6} \right)
For each of the following trigonometric ratios:
Write the ratio in terms of the related acute angle.
Hence, find the exact value of the ratio.
\cos \left( - 210 \degree \right)
\sin 840 \degree
\cos \left( - \dfrac{2 \pi}{3} \right)
\tan \left( \dfrac{7 \pi}{6} \right)
Determine the exact value of the following:
\dfrac{\sin \left(\dfrac{2 \pi}{3}\right) + \cos \left(\dfrac{5 \pi}{6}\right) - \tan \left(\dfrac{7 \pi}{4}\right)}{\cos \left(\dfrac{4 \pi}{3}\right)}
\dfrac{- \sin \left(\dfrac{5 \pi}{3}\right) + \cos \left(\dfrac{7 \pi}{6}\right) + \tan \left(\dfrac{5 \pi}{3}\right)}{- \cos \left(\dfrac{2 \pi}{3}\right)}