Session 17 Warm – up: Find the missing measures. Write all answers in radical form. 30° 45° x 7 10 z 45° w 60° y

TRIGONOMETRY SIN-TAN-COS Math Strategies Ms. Olifer

The Trigonometric Functions we will be looking at SINE COSINE TANGENT

The Trigonometric Functions SINE COSINE TANGENT

SINE Prounounced “sign”

Prounounced “co-sign” COSINE Prounounced “co-sign”

Prounounced “tan-gent”

Represents an unknown angle Greek Letter q Prounounced “theta” Represents an unknown angle

hypotenuse hypotenuse opposite opposite adjacent adjacent

We need a way to remember all of these ratios…

Some Old Hippie Came A Hoppin’ Through Our Old Hippie Apartment

Sin SOHCAHTOA Opp Hyp Cos Adj Hyp Tan Opp Adj Old Hippie

Finding sin, cos, and tan

SOHCAHTOA 10 8 6

10.8 9 A 6 Find the sine, the cosine, and the tangent of angle A. Give a fraction and decimal answer (round to 4 places). 10.8 9 A 6

? 5 4 3 Pythagorean Theorem: (3)² + (4)² = c² 5 = c Find the values of the three trigonometric functions of . ? Pythagorean Theorem: 5 4 (3)² + (4)² = c² 5 = c 3

24.5 8.2 23.1 Find the sine, the cosine, and the tangent of angle A Give a fraction and decimal answer (round to 4 decimal places). B 24.5 8.2 A 23.1

Finding a side

Ex. A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree? tan 71.5° ? tan 71.5° 71.5° y = 50 (tan 71.5°) 50 y = 50 (2.98868)

Ex. 5 A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge? cos 60° x (cos 60°) = 200 200 60° x x X = 400 yards