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This printable supports Common Core Mathematics Standard HSF-TF.C.8

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# Applying the Pythagorean Identity (Grades 11-12)

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## Applying the Pythagorean Identity

1.
Which of the following is an alternate form of the Pythagorean Identity? Choose all correct answers.
1. $tan^2(theta) + sin^2(theta) = 1$
2. $tan^2(theta) + 1 = sec^2(theta)$
3. $1 + sec^2(theta) = cot^2(theta)$
4. $1 + cot^2(theta) = csc^2(theta)$
2.
Given that $cos(theta) = 3/7$ and $0 < theta < pi/2$, what is the value of $sin(theta)?$
1. $(2sqrt(10))/7$
2. $40/49$
3. $sqrt(58)/7$
4. $58/49$
3.
Given that $sin(theta) = -0.56$, find the value of $cos(theta)$, given than $pi < theta < (3pi)/2$. Round the answer to 3 decimal places.
1. -0.828
2. 0.828
3. 0.686
4. -0.686
4.
If $tan(theta) = sqrt(11)/11$ and $pi < theta < (3pi)/2$, what is the value of $sec(theta) ?$
1. $-(2sqrt(33))/11$
2. $sqrt(110)/11$
3. $(2sqrt(33))/11$
4. $-sqrt(110)/11$
5.
If $csc(theta) = -(7sqrt(3))/3$ and $(3pi)/2 < theta < 2pi$, what is the value of $cot(theta) ?$
1. $-sqrt(138)/3$
2. $sqrt(138)/3$
3. $(2sqrt(39))/3$
4. $-(2sqrt(39))/3$
6.
If $tan(theta) = -4/9$ and $pi/2 < theta < pi$, what is the value of $sin(theta) ?$
1. $(4sqrt(97))/97$
2. $sqrt(97)/4$
3. $(9sqrt(97))/97$
4. $(9sqrt(65))/65$
7.
If $sin(theta) = -0.446$ and $(3pi)/2 < theta < 2pi$, what is the value of $tan(theta) ?$ Round the answer to 3 decimal places.
1. -1.899
2. -0.407
3. -0.498
4. 0.498
8.
If $sin(theta) = sqrt(5)/4$ and $pi/2 < theta < pi$, what is the value of $sec(theta) ?$
1. $-sqrt(11)/4$
2. $-(4sqrt(21))/21$
3. $sqrt(11)/4$
4. $-(4sqrt(11))/11$
9.
What is the value of $cos(theta)$ if $cot(theta) = 1/9$ and $pi < theta < (3pi)/2 ?$
1. $-sqrt(82)/82$
2. $-sqrt(10)/10$
3. $-sqrt(5)/20$
4. $-sqrt(2)/4$
10.
What is the value of $tan(theta)$ if $sin(theta) = -3/8$ and $(3pi)/2 < theta < 2pi ?$
1. $-sqrt(55)/3$
2. $-(3sqrt(55))/55$
3. $-sqrt(73)/3$
4. $-(3sqrt(73))/73$
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