Sine, Cosine, and Tangent
Trigonometry is the study of the relationships between the sides and angles of right triangles. The legs are called adjacent or opposite depending on which acute angle is being used.
An easy way to remember ratios is to use SOH-CAH-TOA.
A few important points:
- Always reduce ratios (fractions) when you can.
- Use the Pythagorean Theorem to find the missing side (if there is one).
- If there is a radical in the denominator, rationalize the denominator.
What if you were given a right triangle and told that its sides measure 3, 4, and 5 inches? How could you find the sine, cosine, and tangent of one of the triangle's non-right angles?
First, we need to use the Pythagorean Theorem to find the length of the hypotenuse.
Find the length of the missing side.
Answer the questions about the following image. Reduce all fractions.
Use the diagram to fill in the blanks below.
tanD=?? sinF=?? tanF=?? cosF=?? sinD=?? cosD=??
From questions 1-6, we can conclude the following. Fill in the blanks.
cos−−−−=sinFand sin−−−−=cosF. tanDand tanFare _________ of each other.
To see the Review answers, open this PDF file and look for section 8.7.