Use sine, cosine, and tangent in right triangles, plus the complementary angle relationship and the unit circle.
You relate angles and sides in right triangles using sine, cosine, and tangent. Questions give two sides and ask for a trigonometric ratio, or give a ratio and a side and ask for another side. A recurring pattern uses the relationship that the sine of an angle equals the cosine of its complement, so a question about one angle can be answered from information about the other. You also see angles measured in radians and questions that place an angle on the unit circle.
Trigonometry questions usually appear around 1 to 3 times among the 44 math questions.
Written for this skill, with the answer explained. 99 more are in the app.
In right triangle ABC shown, what is the value of sin A?
In right triangle ABC shown, what is the value of cos A?
Why: First find the hypotenuse: AB = √(8² + 6²) = √100 = 10. For angle A the adjacent leg is AC = 8, so cos A = 8/10 = 4/5. Answering 3/4 is BC/AC = 6/8, which is tan A. Answering 4/3 is that tangent flipped over, and 5/4 inverts the cosine, putting the hypotenuse on top.
In the figure, angle B is a right angle and cos A = 4/5. The hypotenuse AC has length 35. What is the length of AB?
Why: cos A is the adjacent side over the hypotenuse, so AB/35 = 4/5 and AB = 28. Choosing 21 uses 3/5, the sine, which gives the opposite leg BC instead. Answering 21 means you used sin A = 3/5, which gives the opposite leg BC. Answering 43.75 means you divided by 4/5 instead of multiplying by it. Answering 140 means you multiplied by 4 without dividing by 5.
In the figure, angle Q is a right angle and cos P = 0.8. The leg PQ, which is adjacent to angle P, has length 36. What is the length of the hypotenuse PR?
Why: cos P = PQ / PR, so 0.8 = 36 / PR and PR = 36 / 0.8 = 45. Answering 21.6 means you multiplied the leg by 0.8 instead of dividing by it. Answering 27 means you found the other leg QR instead of the hypotenuse. Answering 28.8 means you multiplied by 0.8 instead of dividing by it.
It is the memory aid for the three ratios in a right triangle. Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. Opposite and adjacent are defined relative to the specific angle you are using.
In a right triangle the two non-right angles add to 90 degrees, and the side opposite one of them is adjacent to the other. So the sine of an angle equals the cosine of 90 degrees minus that angle. SAT questions test this relationship directly.
Multiply degrees by pi over 180 to get radians, and multiply radians by 180 over pi to get degrees. A half turn is 180 degrees or pi radians, which is the anchor worth memorizing.
Questions on right triangle trigonometry alone, with explanations on every one, and the app tracks which ones you keep missing.
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