The Basics of Trig. (Sin, Cos, Tan)

The basics of trigonometry allow us to find angle measures and side lengths in a right triangle. (Take note: Basic Trig. only works with a right triangle.) We solve basic Trig. problems using three methods: sine, cosine, and tangent. Sine: sin ø = length of the side opposite the angle length of the hypotenuse (The hypotenuse is a crossed from the right angle) Cosine: cos ø = length of the side adjacent to the angle length of the hypotenuse Tangent: tan ø = length of the side opposite the angle length of the side adjacent to the angle

Area of a Triangle- 1/2•b•c•sinA=1/2•a•c•sinB=1/2•a•b•sinC

Laws of sine- sinA/a=sinB/b=sinC/c a/sinA=b/sinB=c/sinC

Previous Knowledge:

Acute Angle (Less than 90º)

Right Angle (Equal to 90º)

Obtuse Angle (Greater than 90º)

Example: The height of a building is 120 feet. Its shadow is x feet long. The line between the top of the building and the end of the shadow forms a 45º angle. How long is the shadow?We solve this problem by plugging in the values for ø, opp, and hyp. tan 45º = x 120 Solve for x. x = 194.37 feetThe trick to using basic trigonometry to solve problems is to identify which trig. function will solve the problem. The best thing to do is draw a picture and label what you know. The rest comes with practice. With Trigonometry there are several ways to solve a problem in radians, and in degrees. The conversion from degrees to radians is to divide by 180 and multiply by (π).

Conversion From Radians to Degrees

Degrees= (Radians x π) / 180

Conversion From Degrees to Radians

Radians = (Degrees/180) x π

Unit Circles

Making a unit circle can help with very simple, common trig. problems. A unit circle is a plain circle with the degree measurements placed evenly around it with 1 and 360 degrees at the top, showing at common points like 60,90, and 180, the values of the basic trig functions of those degrees in exact form. A basic unit circle looks like this.

Since it is a circle, the measurements repeat after 360 degrees. The values of cos ø and sin ø are the fractions with the squares around the circle. The cos ø values are first in the parentheses, and the sin ø values are second. To get tan ø values you just divide sin ø by cos ø. The values of cos ø from 1-90 and 270-360 will always be positive and from 90-270 it will be always be negative. As for sin ø, from 0-180 the values will always be positive, and from 180-360, the values will always be negative. At 90, cos ø will be 0, at 180, -1, at 270, 0, and at 360, 1. Sin ø does the same thing just not at the same places. Making one of these really helps with remembering the simple trig angles for many problems, and helps a lot with putting the answer in exact form.

To view the graphs of sin, cosine, and tangent, view this link.

http://www.themathpage.com/atrig/graphs-trig.htm#sine%20graph