Recall that we looked at the equation of the unit circle
Today we will we will focus on right triangles.
You are already aquainted with radians and the unit circle. We learned to count by units of π/2, π/3, π/4, π/6, and π itself. If you still need to practice this you should run the Key Radian Values Program more.
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Recall that we looked at the equation of the unit circle Today we will we will focus on right triangles. |
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Recall that the trig functions' definitions (when thought of in terms of the unit circle) are based on the coordinates of the point you land on when you travel a distance of t counterclockwise (for positive t) from the positive x-axis. With this in mind, let's review the values of the six trig functions based on this image: (Put your mouse cursor over the blanks to check your answers.) |  |
Now we need to look at these same trig functions in terms of the similar right triangle below: (Hold your mouse cursor over the blanks to check your answers.)
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Examples 1:
Draw a right triangle and label the legs 5 and 12 units, and label the hypotenuse 13 units. Let α be the angle between the hypotenuse and the the 5 unit leg. Find the six trig functions of α and then click here to check your answers.
Example 2:
Let cos β = 0.25, where β is an acute angle. Use your calculator's inverse cosine key to find an esitimate for β and then estimate the other five trig functions and click here to check your answers.
Example 3: Exact versus Approximation:
The answers in example 2 are approximations since we used a caculator to get them. It is usually preferable to give exact answers whenever possible. Let's redo the example and give exact answers. Start out by using the given information to draw a right triangle and label it. Then use what you've learned in this lecture to calculate the trig functions of β exactly. Click here when you are done to check your answers.