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Name:Date: Page 1of 2Activity 4.6.4Connecticut Core Geometry Curriculum Version 3.0Activity 4.6.4 Complementary Anglesand CofunctionsPart I:Investigating a relationship between Sine and Cosine through tables.1. Using your calculator, complete the following table. 휃sin(휃)cos(휃)9°15°30°45°60°75°81°2. Look for numbers that appear twice in the table and describe any patterns you see.3. Two angles are complementary if the sum of their measures is 90°. Name three pairs of complementary angles in the table above.Part II:Investigating a relationship between Sine and Cosine through a right triangle.4. Using the diagram below, determine each of the following.a.sin(퐴)=b.cos(퐵)=c.sin(퐵)=d.cos(퐴)=5. What do you notice about your answers to 3a and 3b?6. What do you notice about your answers to 3c and 3d?
Name:Date: Page 2of 2Activity 4.6.4Connecticut Core Geometry Curriculum Version 3.07.Complete each of the following equations.a. m ∠A + m ∠퐵=__________b. m ∠A = ___ –m ∠퐵c. m ∠B = ___ –m ∠Ad. ∠A and ∠퐵are called ______________ angles.8.Using your work from Parts I and II, complete the following identities:Suppose 0<휃<90°, where 휃is the measure of an acute angle in a right triangle. sin(휃)=cos(___________)cos(휃)=sin(___________)9.Are there any angle measures for which sin(휃)=cos(휃). Explain.10.Complete each of the following identities.a.sin(42∘)=cos(___________)b.cos(28∘)=sin(___________)c.sin(84∘)=cos(___________)d.cos(67∘)=sin(___________)11.Looking back at the names sine and COsine, why do you think they were given these names?
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