6.04 Radian measure
The diagram shows a number of points on the unit circle:
State the point that corresponds to a distance of \dfrac{\pi}{2} units around the circle.
The diagram shows a number of points on the unit circle:
State the point that corresponds to a distance of \dfrac{21 \pi}{4} units around the circle.
The diagram shows a number of points on the unit circle:
State the point that is closest to a distance of 1.6 radians around the circle.
What fraction of the circumference of the unit circle do the following angles represent?
\dfrac{\pi}{4}
\dfrac{4 \pi}{7}
5 \pi
\dfrac{7 \pi}{2}
The diagram shows the circumference of a unit circle divided into 12 equal arcs, and a number of points on the unit circle.
State two exact angles between - 2 \pi and 2 \pi that correspond to the following points:
S
R
P
Q
State the multiplier to convert an angle from degrees to radians.
State the multiplier to convert an angle from radians to degrees.
Convert the following to radians, giving your answers in exact form:
180 \degree
360 \degree
90 \degree
30 \degree
60 \degree
210 \degree
45 \degree
225 \degree
112 \degree
- 300 \degree
- 270 \degree
- 135 \degree
Convert the following to radians, correct to two decimal places:
29 \degree
161.17 \degree
321 \degree 31 '
234 \degree 09 '
Convert the following angles in radians to degrees, correct to one decimal place when necessary:
\dfrac{\pi}{3}
\dfrac{2 \pi}{3}
- \dfrac{5 \pi}{3}
4.2
Consider the location of the angle on the unit circle and hence state the exact values of the following:
\sin \pi
\sin \dfrac{\pi}{2}
\tan 9 \pi
\cos 4 \pi
Consider the trigonometric ratio \sin \dfrac{5 \pi}{6}.
Determine the quadrant in which \dfrac{5 \pi}{6} is located.
Hence state whether \sin \dfrac{5 \pi}{6} is positive or negative.
Find the positive acute angle that \dfrac{5 \pi}{6} is related to.
Hence rewrite \sin \dfrac{5 \pi}{6} in terms of its related acute angle.
Consider the trigonometric ratio \cos \dfrac{5 \pi}{4}.
Determine the quadrant in which \dfrac{5 \pi}{4} is located.
Hence state whether \cos \dfrac{5 \pi}{4} is positive or negative.
Find the positive acute angle that \dfrac{5 \pi}{4} is related to.
Hence rewrite \cos \dfrac{5 \pi}{4} in terms of its related acute angle.
Consider the trigonometric ratio \tan \dfrac{5 \pi}{3}.
Determine the quadrant in which \dfrac{5 \pi}{3} is located.
Hence state whether \tan \dfrac{5 \pi}{3} is positive or negative.
Find the positive acute angle that \dfrac{5 \pi}{3} is related to.
Hence rewrite \tan \dfrac{5 \pi}{3} in terms of its related acute angle.
Consider the angle \dfrac{2 \pi}{3}.
Determine the quadrant in which the angle is located.
Express the following ratios in terms of a related acute angle:
Consider the angle \dfrac{7 \pi}{6}.
Determine the quadrant in which the angle is located.
Express the following ratios in terms of a related acute angle:
Using the approximations \cos \dfrac{\pi}{3} = 0.50, and \sin \dfrac{\pi}{3} = 0.87, write down the approximate value of the following, correct to two decimal places:
\cos \left(-\dfrac{ \pi}{3} \right)
\sin \left(-\dfrac{ \pi}{3} \right)
\cos \dfrac{2 \pi}{3}
\sin \left( - \dfrac{4 \pi}{3} \right)
Using the approximations \cos \dfrac{\pi}{5} = 0.81, and \sin \dfrac{\pi}{5} = 0.59, write down the approximate value of the following, correct to two decimal places:
Suppose s is a real number that corresponds to the point \left( - \dfrac{5}{13} , \dfrac{12}{13}\right) on the unit circle:
State the exact value of \sin \left(s + 6 \pi\right).
State the exact value of \cos \left(s + 6 \pi\right).
Suppose p is a real number that corresponds to the point \left( - \dfrac{4}{5} , \dfrac{3}{5}\right) on the unit circle:
Find the exact value of \sin \left( - p \right).
Find the exact value of \cos \left( - p \right).
Suppose q is a real number that corresponds to the point \left( - \dfrac{15}{17} , \dfrac{8}{17}\right) on the unit circle:
Find the exact value of \sin \left(q + \pi\right).
Find the exact value of \cos \left(q + \pi\right).