Question

assignment 9.1: trigonometric
score: 1/20 answered: 1/16
question 2
simplify \\( \frac{\tan (t)}{\sec (t)} \\) to a single trig function.
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Explanation:

Step1: Substitute trigonometric identities

We know that \(\tan(t)=\frac{\sin(t)}{\cos(t)}\) and \(\sec(t)=\frac{1}{\cos(t)}\).
So, \(\frac{\tan(t)}{\sec(t)}=\frac{\frac{\sin(t)}{\cos(t)}}{\frac{1}{\cos(t)}}\).

Step2: Simplify the expression

When we divide by a fraction, we multiply by its reciprocal. So \(\frac{\frac{\sin(t)}{\cos(t)}}{\frac{1}{\cos(t)}}=\frac{\sin(t)}{\cos(t)}\times\cos(t)\).
The \(\cos(t)\) terms cancel out, leaving \(\sin(t)\).

Answer:

\(\sin(t)\)