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education/math/MATH1060 (trig)/Identities.md
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@ -42,7 +42,7 @@ $$ sin^2\theta $$
### Finding all values using identities ### Finding all values using identities
If $sec\theta = -\frac{25}{7}$ and $0 < \theta < \pi$, find the values of the other 5 trig functions: If $sec\theta = -\frac{25}{7}$ and $0 < \theta < \pi$, find the values of the other 5 trig functions:
Using the trig identity $1 + tan^2\theta = cot^2\theta$, we can do this: 1. To find $tan\theta$, we can use the trig identity $1 + tan^2\theta = sec^2\theta$:
$$ 1 + tan^2\theta = (-\frac{25}{7})^2 $$ $$ 1 + tan^2\theta = (-\frac{25}{7})^2 $$
Shuffling things around, we get this: Shuffling things around, we get this:
$$ tan^2\theta = \frac{625}{49} - 1 $$ $$ tan^2\theta = \frac{625}{49} - 1 $$
@ -54,3 +54,5 @@ You can get rid of the exponent:
$$ \sqrt{\frac{576}{49}} = tan\theta $$ $$ \sqrt{\frac{576}{49}} = tan\theta $$
$\sqrt{576} = 24$ and $\sqrt{49} = 7$, so: $\sqrt{576} = 24$ and $\sqrt{49} = 7$, so:
$$ tan\theta = \frac{24}{7} $$ $$ tan\theta = \frac{24}{7} $$
2. To find $cos\theta$, because $sec$ is the inverse of $cos$, we can use the identity $sec\theta = \frac{1}{cos\theta}$:
So $cos\theta = -\frac{7}{25}$.