diff --git a/education/math/MATH1060 (trig)/Identities.md b/education/math/MATH1060 (trig)/Identities.md index 2eb431d..63f13d8 100644 --- a/education/math/MATH1060 (trig)/Identities.md +++ b/education/math/MATH1060 (trig)/Identities.md @@ -42,7 +42,7 @@ $$ sin^2\theta $$ ### Finding all values using identities 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 $1 + tan^2\theta = sec^2\theta$: $$ 1 + tan^2\theta = (-\frac{25}{7})^2 $$ Shuffling things around, we get this: $$ tan^2\theta = \frac{625}{49} - 1 $$ @@ -54,3 +54,5 @@ You can get rid of the exponent: $$ \sqrt{\frac{576}{49}} = tan\theta $$ $\sqrt{576} = 24$ and $\sqrt{49} = 7$, so: $$ tan\theta = \frac{24}{7} $$ +2. To find $cos\theta$, because $sec$ is the inverse of $cos$, we can use the identity $sec\theta = \frac{1}{cos\theta}$: +So $cos\theta = -\frac{7}{25}$. \ No newline at end of file