Hold on though. Check THIS out…
Amazing.
Trigonometry might sound like a mouthful, but when it comes to finding the cosine, sine, or tangent of an angle on the SAT, it’s just about working with triangles. Sometimes the test gives you the value of one trig function (like cosine, sine, or tangent) and asks you to find another trig function for a different angle in the same triangle. Don’t worry—it’s less scary than it sounds. With a little help from the Pythagorean Theorem and some basic formulas, you’ve got this!
And if test anxiety or SAT anxiety starts to creep in, just take a deep breath and remember: this is all about triangles, and triangles are your friends.
Know Your Trig Basics
Before we jump into solving problems, let’s review the three big trig functions:
These formulas come from a right triangle, where:
- The hypotenuse is the longest side (the one opposite the right angle).
- The opposite side is the one across from the angle you’re working with.
- The adjacent side is the one next to your angle (but not the hypotenuse).
Use the Pythagorean Theorem
The Pythagorean Theorem says:
Where:
- a and b are the two shorter sides of the triangle (the legs).
- c is the hypotenuse (the longest side).
This is your go-to tool for finding missing sides in right triangles. Once you have all three sides, you can calculate sin, cos, or tan for any angle in the triangle.
An Example
Let’s break it down with an example SAT-style problem:
Step 2: Use the Pythagorean Theorem
Step 4: What About the Other Angle?
If the problem asks for cos, sin, or tan of the other angle in the triangle, it’s just about flipping roles!
In the same triangle, the angles are complementary, meaning they add up to 90°. So if you know one angle’s trig values, the other’s are reversed:
- The adjacent side for one angle becomes the opposite side for the other.
- The opposite side for one angle becomes the adjacent side for the other.
Test Anxiety Tip: Take It Step by Step
If SAT anxiety has you worried about trig problems, just focus on these steps:
- Identify what you know: Write down the given trig value and what it represents (opposite, adjacent, or hypotenuse).
- Use the Pythagorean Theorem: Solve for the missing side if needed.
- Plug into the formulas: Use the definitions of sine, cosine, or tangent to find the value you need.
Remember, these problems are just puzzles waiting for you to connect the pieces.
Final Thoughts
Finding cos, sin, or tan for an angle when you’re given one of them isn’t as tricky as it seems. With the Pythagorean Theorem and a little patience, you can calculate any missing values and ace these problems on the SAT.
Keep practicing, and if you need more tips to tackle SAT math with confidence, check back in with this blog. We’ve got plenty of strategies to help you beat test anxiety and rock your SAT! Good luck, and go show those triangles who’s boss!