Name: _____________________________________
Date: _____________________
PreCalc
Discovery Activity – Section 10.1
Throughout this activity, you will discover even more relationships between sine and cosine!
Complete the following statements involving sine and cosine:
𝐬𝐢𝐧 𝟑𝟎° =
𝐬𝐢𝐧 𝟒𝟓° =
𝐬𝐢𝐧 𝟔𝟎° =
𝐬𝐢𝐧 𝟗𝟎° =
𝐜𝐨𝐬 𝟑𝟎° =
𝐜𝐨𝐬 𝟒𝟓° =
𝐜𝐨𝐬 𝟔𝟎° =
𝐜𝐨𝐬 𝟗𝟎° =
For the purposes of the following exercises, let 𝑨 = 𝟑𝟎°, 𝑩 = 𝟒𝟓°, 𝑪 = 𝟔𝟎°, 𝒂𝒏𝒅 𝑫 = 𝟗𝟎°.
cos(𝐴 + 𝐴) =
cos(𝐴 + 𝐶) =
cos(𝐶 − 𝐴) =
cos(𝐷 − 𝐵) =
cos 𝐴 ∙ cos 𝐴 =
cos 𝐴 ∙ cos 𝐶 =
cos 𝐶 ∙ cos 𝐴 =
cos 𝐷 ∙ cos 𝐵 =
sin 𝐴 ∙ sin 𝐴 =
sin 𝐴 ∙ sin 𝐶 =
sin 𝐶 ∙ sin 𝐴 =
sin 𝐷 ∙ sin 𝐵 =
Do you see any relationship between the three numbers you result in for each column??
(If so, describe that relationship below)
SUMMARY: How can we generalize our findings?
Use your calculator to test 3 more pairs of angle sums:
Name: _____________________________________
Date: _____________________
PreCalc
BRAINSTORM:
Do you think the same relationship occurs for sin(𝐴 + 𝐵)? WHY or WHY NOT?
Complete the following statements involving sine and cosine:
𝐬𝐢𝐧 𝟑𝟎° =
𝐬𝐢𝐧 𝟒𝟓° =
𝐬𝐢𝐧 𝟔𝟎° =
𝐬𝐢𝐧 𝟗𝟎° =
𝐜𝐨𝐬 𝟑𝟎° =
𝐜𝐨𝐬 𝟒𝟓° =
𝐜𝐨𝐬 𝟔𝟎° =
𝐜𝐨𝐬 𝟗𝟎° =
For the purposes of the following exercises, let 𝑨 = 𝟑𝟎°, 𝑩 = 𝟒𝟓°, 𝑪 = 𝟔𝟎°, 𝒂𝒏𝒅 𝑫 = 𝟗𝟎°.
sin(𝐴 + 𝐴) =
sin(𝐴 + 𝐶) =
sin(𝐶 − 𝐴) =
sin(𝐷 − 𝐵) =
cos 𝐴 ∙ sin 𝐴 =
cos 𝐴 ∙ sin 𝐶 =
cos 𝐶 ∙ sin 𝐴 =
cos 𝐷 ∙ sin 𝐵 =
sin 𝐴 ∙ cos 𝐴 =
sin 𝐴 ∙ cos 𝐶 =
sin 𝐶 ∙ cos 𝐴 =
sin 𝐷 ∙ cos 𝐵 =
Do you see any relationship between the three numbers you result in for each column??
(If so, describe that relationship below)
SUMMARY: How can we generalize our findings?
Use your calculator to test 3 more pairs of angle sums: