mit 7 Revew (men Ratios) Doorvank (2) BLAKE SINDAM 22 Consider the trigonometric expression about one acute angle of a right triangle. Which expression is equivalent? $$ \sin (y-10)^{\circ} $$ (A) $$ 1-\cos (80-y)^{\circ} $$ (B) $$ \cos (100-i)^{\circ} $$ (C) $$ 1-\sin (100-y)^{\circ} $$ (D) $$ \sin (170-y)^{\circ} $$

Question

UpStudy AI · Accepted Answer

To find an equivalent expression for $$ \sin (y-10)^{\circ} $$, we can use trigonometric identities and properties. Let's analyze each option step by step.

1. **Original Expression**: 
   $$
   \sin (y-10)^{\circ}
   $$

2. **Option (A)**: $$ 1 - \cos (80 - y)^{\circ} $$

We can use the identity $$ \sin^2 A + \cos^2 A = 1 $$ to rewrite this:
   $$
   1 - \cos (80 - y)^{\circ} = \sin^2 (80 - y)^{\circ}
   $$
   This does not simplify to $$ \sin (y-10)^{\circ} $$.

3. **Option (B)**: $$ \cos (100 - y)^{\circ} $$

Using the co-function identity $$ \sin A = \cos (90 - A) $$:
   $$
   \sin (y-10)^{\circ} = \cos (90 - (y-10))^{\circ} = \cos (100 - y)^{\circ}
   $$
   This matches, so this option is equivalent.

4. **Option (C)**: $$ 1 - \sin (100 - y)^{\circ} $$

This does not relate to $$ \sin (y-10)^{\circ} $$ through any standard identities.

5. **Option (D)**: $$ \sin (170 - y)^{\circ} $$

Using the identity $$ \sin (180 - A) = \sin A $$:
   $$
   \sin (170 - y)^{\circ} = \sin (180 - (y + 10))^{\circ} = \sin (y + 10)^{\circ}
   $$
   This does not match $$ \sin (y-10)^{\circ} $$.

After analyzing all options, the equivalent expression for $$ \sin (y-10)^{\circ} $$ is:

**Answer**: (B) $$ \cos (100 - y)^{\circ} $$
The equivalent expression is $$ \cos (100 - y)^{\circ} $$.

Real Tutor Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Trigonometry Questions