Trig Signs
About This Worksheet
This worksheet helps twelfth-grade Pre-Calculus students practice determining whether sine, cosine, and tangent are positive or negative in each quadrant. Students work through ten angles written in degrees and radians. For each one, they first identify the quadrant and then determine the sign of all three main trig functions.
The focus is not on finding exact numerical values. Instead, students build a stronger understanding of how the location of an angle controls the sign of its trig values.
What Students Practice
Students practice using the coordinate-plane meaning of sine and cosine. Cosine follows the horizontal coordinate, while sine follows the vertical coordinate. Tangent depends on the signs of both.
The worksheet helps students see the repeating quadrant pattern. In the first quadrant, all three are positive. In the second, sine is positive. In the third, tangent is positive. In the fourth, cosine is positive.
Students also practice locating angles in both degree and radian form before deciding on the signs.
Why This Skill Matters
Knowing trig signs is essential when students work with reference angles. A student may know the correct basic value but still get the final answer wrong if the sign does not match the quadrant.
This skill also helps with solving trig equations, graphing trig functions, and understanding unit-circle coordinates.
Common Challenges
Students may memorize the sign pattern without connecting it to coordinates. Remind them that cosine behaves like the x-coordinate and sine behaves like the y-coordinate. That gives them a way to rebuild the signs if they forget.
Another common mistake is deciding the sign before locating the angle. Encourage students to identify the quadrant first.
Students may also forget that tangent is positive when sine and cosine have the same sign and negative when they have opposite signs.
How To Use It
Teachers can use this worksheet after reference-angle practice. It works well for independent review, homework, warm-up work, or preparation for exact trig-value problems.
Parents and homeschool teachers can ask, “Is the point left or right of the vertical axis?” and “Is it above or below the horizontal axis?” Those answers reveal the signs of cosine and sine, which then help with tangent.
Grade Alignment
This Grade 12 Pre-Calculus worksheet supports understanding of trig signs across all four quadrants. It reinforces the relationship among unit-circle position, coordinates, and trig values.
Students should already know how to locate angles by quadrant. After this practice, they can move into analyzing sine and cosine functions by their graph features.