Q: What is express in one function?

$\sin^2 \theta = 1 - \cos^2 \theta$, and $\cos^2 \theta = 1 - \sin^2 \theta$. Useful for rewriting an expression in a single trig function before solving.

Q: What is difference of squares?

$1 - \sin^2 \theta = (1-\sin\theta)(1+\sin\theta) = \cos^2\theta$.

Q: What is combine over a common denominator?

$\frac{1}{\cos\theta} - \cos\theta = \frac{1 - \cos^2\theta}{\cos\theta} = \frac{\sin^2\theta}{\cos\theta} = \sin\theta \tan\theta$.

Q: What is forgetting the sign?

$\sin^2 \theta + \cos^2 \theta = 1$ gives a positive value for each square. The sign of the trig function itself comes from the quadrant.

Q: What is treating $\sin^2 \theta$ as $\sin \theta^2$?

$\sin^2 \theta$ means $(\sin\theta)^2$. The squared notation is conventional; do not confuse it with $\sin(\theta^2)$.

Q: What is dividing by $\cos\theta$ without checking $\cos\theta = 0$?

When $\cos\theta = 0$, dividing loses solutions. Always check the endpoint solutions separately.

Question 1

What is express in one function?

Accepted Answer

$\sin^2 	heta = 1 - \cos^2 	heta$, and $\cos^2 	heta = 1 - \sin^2 	heta$. Useful for rewriting an expression in a single trig function before solving.

Question 2

What is difference of squares?

Accepted Answer

$1 - \sin^2 	heta = (1-\sin	heta)(1+\sin	heta) = \cos^2	heta$.

Question 3

What is combine over a common denominator?

Accepted Answer

$\frac{1}{\cos	heta} - \cos	heta = \frac{1 - \cos^2	heta}{\cos	heta} = \frac{\sin^2	heta}{\cos	heta} = \sin	heta 	an	heta$.

Question 4

What is forgetting the sign?

Accepted Answer

$\sin^2 	heta + \cos^2 	heta = 1$ gives a positive value for each square. The sign of the trig function itself comes from the quadrant.

Question 5

What is treating $\sin^2 	heta$ as $\sin 	heta^2$?

Accepted Answer

$\sin^2 	heta$ means $(\sin	heta)^2$. The squared notation is conventional; do not confuse it with $\sin(	heta^2)$.

Question 6

What is losing solutions during factoring?

Accepted Answer

Always set each factor to zero and find all solutions in the stated interval before deciding which to accept.

Question 7

What is dividing by $\cos	heta$ without checking $\cos	heta = 0$?

Accepted Answer

When $\cos	heta = 0$, dividing loses solutions. Always check the endpoint solutions separately.