# Download Section 17.2 Define and evaluate basic trigonometric functions.

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```Section 17.2 Define and evaluate basic trigonometric functions. (2 Days)
1) Draw the triangles above using radians instead of degrees.
2) Draw the triangles above if a = 1
3)Draw the triangles above if the hypotenuse is 1.
Using the angles of rotation which we discussed last class we are able to extend the domain of the trig functions beyond the
invterval (0,90°) or (0, ) and therefore ask for the value of something like sin(120°) or
.
To find the correct triangle when evaluating sin(θ), we will need to draw the angle θ in standard position. Then draw a vertical
segment connecting the terminal point of the terminal side with the x-axis.
For each: Draw a picture that includes the angle in standard positon, a special right triangle, and a reference angle(if the angle is
greater than 90° or less than -90°), then evaluate each without a calculator.
4) sin(300°)
13) tan −
5)cos(120°) 6) tan( ) 7) sin
14) sin(−240°)
8) cos
9) tan(120°) 10)sin
11)tan(210°)
12) cos −
When we consider only triangles with a hypotenuse of 1. The terminal point of each terminal
side for all angles will trace out what is called the unit circle.(Unit meaning 1. See provided paper) On the unit circle the x
coordinate of the point will be the cosθ and the y coordinate with be the sinθ. The unit circle is not needed to do the above
problems but it is helpful when evaluating the trig functions for quadrantal angles. These are angles in which the terminal side lies
on the x or y axis. such as 180°, or .
Evaluate each. 15)sin(540°) 16)
17) sin( ) 18)cos(2 )
19) An airplane begins to descend toward a runway 1 mile away at an angle of -5° to the horizontal. What is its change in elevation after flying 5000
feet horizontally towards the run way?
20) How long a shadow does a 40 foot tall tree cast on the ground if the sun is at an angle of .5 radians relative to the horizon?
Section 17.2 Define and evaluate basic trigonometric functions. (2 Days)
1) Draw the triangles above using radians instead of degrees.
2) Draw the triangles above if a = 1
3)Draw the triangles above if the hypotenuse is 1.
Using the angles of rotation which we discussed last class we are able to extend the domain of the trig functions beyond the
invterval (0,90°) or (0, ) and therefore ask for the value of something like sin(120°) or
.
To find the correct triangle when evaluating sin(θ), we will need to draw the angle θ in standard position. Then draw a vertical
segment connecting the terminal point of the terminal side with the x-axis.
For each: Draw a picture that includes the angle in standard positon, a special right triangle, and a reference angle(if the angle is
greater than 90° or less than -90°), then evaluate each without a calculator.
4) sin(300°)
13) tan −
5)cos(120°) 6) tan( ) 7) sin
14) sin(−240°)
8) cos
9) tan(120°) 10)sin
11)tan(210°)
12) cos −
When we consider only triangles with a hypotenuse of 1. The terminal point of each terminal
side for all angles will trace out what is called the unit circle.(Unit meaning 1. See provided paper) On the unit circle the x
coordinate of the point will be the cosθ and the y coordinate with be the sinθ. The unit circle is not needed to do the above
problems but it is helpful when evaluating the trig functions for quadrantal angles. These are angles in which the terminal side lies
on the x or y axis. such as 180°, or .
Evaluate each. 15)sin(540°) 16)
17) sin( ) 18)cos(2 )
19) An airplane begins to descend toward a runway 1 mile away at an angle of -5° to the horizontal. What is its change in elevation after flying 5000
feet horizontally towards the run way?
20) How long a shadow does a 40 foot tall tree cast on the ground if the sun is at an angle of .5 radians relative to the horizon?
```
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