Trigonometry The study of triangles sides and angles

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Trigonometry: The study of triangles (sides and angles) Trigonometry has been used for centuries

Trigonometry: The study of triangles (sides and angles) Trigonometry has been used for centuries in the study of: astronomy surveying geography engineering www. thevisualclassroom. com physics

B e s u n e t o p hy A www. thevisualclassroom. com

B e s u n e t o p hy A www. thevisualclassroom. com adjacent opposite C

B e s u n e t o p y adjacent h A www.

B e s u n e t o p y adjacent h A www. thevisualclassroom. com opposite C

B e t o opposite adjacent C p y h A www. thevisualclassroom. com

B e t o opposite adjacent C p y h A www. thevisualclassroom. com e s nu

B e s u n e t o p y h A www. thevisualclassroom.

B e s u n e t o p y h A www. thevisualclassroom. com opposite adjacent C

B p y h A adj opp C SOH CAH TOA www. thevisualclassroom. com

B p y h A adj opp C SOH CAH TOA www. thevisualclassroom. com

10 A www. thevisualclassroom. com B hy p SOH CAH TOA 6 8 C

10 A www. thevisualclassroom. com B hy p SOH CAH TOA 6 8 C adj opp

B hyp SOH CAH TOA 5 A www. thevisualclassroom. com 3 4 opp C

B hyp SOH CAH TOA 5 A www. thevisualclassroom. com 3 4 opp C adj

SOH CAH TOA hy p B 13 5 adj A www. thevisualclassroom. com 12

SOH CAH TOA hy p B 13 5 adj A www. thevisualclassroom. com 12 opp C

Use a calculator to determine the following ratios. sin 21° = 0. 3584 cos

Use a calculator to determine the following ratios. sin 21° = 0. 3584 cos 53° = 0. 6018 tan 72° = 3. 0777 www. thevisualclassroom. com

Determine the following angles (nearest degree). sin A = 0. 4142 ÐA = sin-1(0.

Determine the following angles (nearest degree). sin A = 0. 4142 ÐA = sin-1(0. 4142) = 24° cos B = 0. 6820 ÐB = cos-1(0. 6820) = 47° tan C = 1. 562 ÐC = tan-1(1. 562) = 57° www. thevisualclassroom. com

Determine the following angles (nearest degree). sin A = = 0. 5833 cos B

Determine the following angles (nearest degree). sin A = = 0. 5833 cos B = = 0. 2666 tan C = = 1. 875 www. thevisualclassroom. com ÐA = sin-1(0. 5833) = 36° ÐB = cos-1(0. 2666) = 75° ÐC = tan-1(1. 875) = 62°

Example 1: Determine side a hyp SOH CAH TOA A B m c 6

Example 1: Determine side a hyp SOH CAH TOA A B m c 6 opp a 30º C a = 6 sin 30° a = 6 (0. 5) a = 3 cm www. thevisualclassroom. com

Ex. 2: Name two trig ratios that will allow us to calculate side b.

Ex. 2: Name two trig ratios that will allow us to calculate side b. 9 m B 50º 40º A www. thevisualclassroom. com b C

Example 3: Determine side b B 55º SOH CAH TOA 8 cm A b

Example 3: Determine side b B 55º SOH CAH TOA 8 cm A b = 8 tan 55° b = 8 (1. 428) b = 11. 4 cm www. thevisualclassroom. com ad C j b opp

Example 4: Determine the measure of ÐP. t n e c cm ÐP =

Example 4: Determine the measure of ÐP. t n e c cm ÐP = cos– 1(0. 70588) Q m c 7 1 ÐP = 45. 1° P www. thevisualclassroom. com R 12 cos P = 0. 70588 adja SOH CAH TOA o p y h e s u ten

Example 5: Determine the measure of side PR. opp adj R q 12 cm

Example 5: Determine the measure of side PR. opp adj R q 12 cm Method 1 q(tan 35°) = 12 35° Q q = 17. 1 cm www. thevisualclassroom. com P

q 12 ÐQ = 55° cm Example 6: Determine the measure of side PR.

q 12 ÐQ = 55° cm Example 6: Determine the measure of side PR. Method 2 adj opp R ÐQ = 90° – 35° q = 12(tan 55°) q = 12(1. 428) q = 17. 1 cm www. thevisualclassroom. com Q 55° 35° P

Ex. 7: In DPQR, ÐQ = 90°. R 8 c m a) Find sin

Ex. 7: In DPQR, ÐQ = 90°. R 8 c m a) Find sin R if PR = 8 cm and PQ = 4 cm. b) Find cos R. RQ 2 = 82 – 42 RQ 2 = 64 – 16 RQ 2 = 48 www. thevisualclassroom. com P 4 cm Q