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8-4 Sine, Cosine, and Tangent Ratios Chapter 8 Section 4 Mrs. Brook.

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Presentation on theme: "8-4 Sine, Cosine, and Tangent Ratios Chapter 8 Section 4 Mrs. Brook."— Presentation transcript:

1 8-4 Sine, Cosine, and Tangent Ratios Chapter 8 Section 4 Mrs. Brook

2 Vocabulary Trigonometry Derived from Greek words meaning “triangle measurement”

3 Triangle terminology

4 Opposite side: the side opposite the angle angle opposite angle

5 Adjacent side: the side beside the angle adjacent angle

6 Hypotenuse: the longest side and across from the right angle hypotenuse

7 SOH CAH TOA SOH CAH TOA You need to memorize this!!! Use SOH CAH TOA to help you remember these ratios!!!

8 Definitio ns A B 90 o C a c b

9 Sine of angle A A B 90 o C a c b sin(A) == acac opposite hypotenuse

10 Sine of angle B A B 90 o C a c b sin(B) == bcbc opposite hypotenuse

11 Cosine of angle A A B 90 o C a c b cos(A) == bcbc adjacent hypotenuse

12 Cosine of angle B A B 90 o C a c b cos(B) == acac adjacent hypotenuse

13 Tangent of angle A A B 90 o C a c b tan(A) = opposite adjacent abab =

14 Tangent of angle B A B 90 o C a c b tan(B) = opposite adjacent baba =

15 Write the Sin, Cos, and Tan Ratios for angle A A B C SOH CAH TOA Sin A = 7/25 Cos A = 24/25 Tan A = 7/24

16 Try this one Sin E Cos E Tan E Sin F Cos F Tan F SOH CAH TOA 6/10 = 3/5 8/10 = 4/5 6/8 = 3/4 8/10 = 4/5 6/10 = 3/5 8/6 = 4/3

17 Find the value of x using Trig. Note: If “x” is on top - multiply; If “x” is on bottom - divide!! 64 7 X THIS IS JUST THE ANGLE!! Remember: SOH CAH TOA Since we have an O & A we use Tan (no hypotenuse!) Tan 64 = x/7 Since x is on top, mult. Type 7 * tan 64 in calc. 67 x X x Since we have an O & A we use Tan (no hypotenuse!) Tan 67 = 6/x Since we have an O & H we use Sin Sin 35 = x/20 Since we have an A & H we use Cos Cox 62 = 50/x Since x is on bottom divide. Type 6 divided by tan 67 in calc Since x is on top, mult. Type 20 * sin 35 in calc. Since x is on bottom divide Type 50 divided by cos 62 in calc.

18 Find the value of x degrees using Trig. Note: When finding an angle measure use “inverse” Trig. or the 2nd button!! x 3 9 ____ x x ____ 4 5 Remember: SOH CAH TOA Since we have an O & A we use Tan (no hypotenuse!) Tan x = 9/3 Since we have an A & H we use Cos Cos x = 16/20 Since we have an O & H we use Sin Sin x = 4/5 Since x is the angle, use the 2nd button! Type 2nd Tan, then 9/3 using the n/d button. Since x is the angle, use the 2nd button! Type 2nd Cos, then 16/20 using the n/d button. Since x is the angle, use the 2nd button! Type 2nd Sin, then 4/5 using the n/d button

19 What have I learned? SOH CAH TOA If “x” is on bottom “divide” If “x” is on top “multiply” If solving for a side use regular sin, cos, or tan If solving for an angle use inverse sin, cos, or tan

20 Here’s your daily joke Why didn’t sin and tan go to the party? Just cosHa! Ha!

21


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