Right Triangles and Trig Ratios

SOH-CAH-TOA

• SOH-CAH-TOA is an acronym used in Geometry and Right Triangle Trig to remember what sides of a right triangle go with which Trig Ratios

• Each angle value (radians and degrees) has a specific ratio of sides that always holds true

Consider an angle whose terminal ray passes through the point (4, 5)

• In which quadrant does this angle fall?• Tell whether the sine, cosine and tangent are

positive or negative for this angle (in Q1)

Consider an angle whose terminal ray passes through the point (-4, 5)

• In which quadrant does this angle fall?• Tell whether the sine, cosine and tangent are

positive or negative for this angle (in Q2)

Consider an angle whose terminal ray passes through the point (-4, -5)

• In which quadrant does this angle fall?• Tell whether the sine, cosine and tangent are

positive or negative for this angle (in Q3)

Consider an angle whose terminal ray passes through the point (4, -5)

• In which quadrant does this angle fall?• Tell whether the sine, cosine and tangent are

positive or negative for this angle (in Q4)

Trig Definitions/Ratios

• Since the opposite always refers to the vertical distance and the adjacent always refers to the horizontal distance, we can say that…

r

ysin

r

xcos

x

ytan

Sign Analysis Chart

Examples

• Tell whether each of the following is positive or negative:

240sin

Examples

• Tell whether each of the following is positive or negative:

240sin 300cos

Examples

• Tell whether each of the following is positive or negative:

240sin 300cos

4

3tan

Examples

• Tell whether each of the following is positive or negative:

240sin 300cos

4

3tan

3

4sin

Finding Exact Values

• If is a 4th quadrant angle and , find and

12

5tan

sin cos

Finding Exact Values

• An angle has a terminal ray that passes through the point (-4, 7). Find the exact value of the three trig ratios in simplest form.

The Unit Circle(Quadrantal Angles)

• Consider a circle with radius = ____– What is the sin 90?

– Does the size of the circle matter when evaluating the trig ratios?

The Unit Circle(Quadrantal Angles)

Examples

• Find the exact value for each of the following:270sin

Examples

• Find the exact value for each of the following:270sin 90tan

Examples

• Find the exact value for each of the following:270sin 90tan

cos

Examples

• Find the exact value for each of the following:270sin 90tan

cos

2

5sin

Homework

• Pg. 272 (1 – 27odd)