For many students, the mere word “trigonometry” can be intimidating and discouraging. Looming at the end of most high school geometry and algebra II curricula, trig can feel insurmountable. With thoughtful study, however, this subject can become yet another comfortable tool in your academic arsenal. Here are 6 trigonometry tips that can help boost your math mastery:
One: An alternative way to write SOHCAHTOA
When asked what they remember about learning trigonometry in school, many people are able to recall the acronym SOHCAHTOA. Some may even recall what the letters stand for: Sine Opposite Hypotenuse, Cosine Adjacent Hypotenuse, Tangent Opposite Adjacent. However, the acronym alone may not be enough to jog one’s memory of the ratios being described.
To better reinforce this relationship between the acronym and the ratios, here is an alternative way of writing SOHCAHTOA:
Notice the visual representation of the math involved. “SOH” represents “Sine (of an angle) = Opposite over Hypotenuse.” Written as shown, that relationship is made clear and memorable.
Two: Your prior right triangle knowledge still applies!
Much of trig interacts with geometry rules you likely already know. Think of the triangle rules you’ve come to rely on: the sum of their interior angles is 180°, and the sum of the squares of the legs is the square of the hypotenuse. These facts will prove useful in many trigonometry problems, such as the following:
What is the sine of angle B in the right triangle below if measures 3 and measures 4?*
Consider how essential the Pythagorean theorem will be in a problem like this.
Three: Think of identities as translation problems.
If you’re having difficulties remembering trig identities such as , try translating the ratio names back into the ratios they represent, like so:
Notice anything? Opposite and Adjacent are names for the legs of a right triangle. Thus, they can fill in for a and b in the Pythagorean Theorem. Therefore:
Developing a stronger sense of the math reasoning behind trigonometric statements like the identities will reinforce your understanding of them.
Four: Change your perspective (and angle)!
Sometimes, the right answer on a multiple-choice test will use a different angle than what you’ve been given in the question. As mentioned in Tip #2, remember your knowledge of triangles. If you are told that a right triangle includes an angle of 48°, you can deduce that the remaining angle measures 42°, which may be necessary to select the correct answer.
Five: Trig can be used for non-right triangles, too.
Trig isn’t just limited to right triangles: the Law of Sines and the Law of Cosines are applicable to all triangles.
For a triangle with side lengths a, b, and c and interior angles opposite those respective sides measuring A, B, and C, the Law of Sines states:
For a triangle with side lengths a, b, and c and interior angles opposite those respective sides measuring A, B, and C, the Law of Cosines states:
Six: Trigonometry doesn’t have to be limited to problems explicitly involving triangles.
Any shape can be decomposed into a series of triangles, making trigonometry’s utility expand beyond triangles alone. Consider how trigonometry could be used to solve the problem below:
Given a parallelogram ABCD with a height of 8, (AD) ̅ measuring 10, and (DC) ̅ measuring 18, what is the tangent of angle CBA?**
These are just a few trigonometry tips and techniques that can help bolster your understanding of this Geometry subtopic and increase your math mastery.
No matter your comfortability with trigonometry (or math in general), at Academic Approach we promise to break down challenging topics in a way that speaks to you—that’s part of our promise in offering customized one-on-one tutoring. Call today to start your tutoring journey with us!
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* = The sine of angle B is 4/5. The hypotenuse can be found by plugging the lengths of the triangle’s legs into the Pythagorean Theorem.
** = The tangent of angle CBA is 4/3. Imagine drawing a vertical line starting from point C and ending at side (AB) ̅, forming a right triangle with (BC) ̅ as the hypotenuse. Given that (BC) ̅ must measure 10 and the height of the parallelogram is 8, use the Pythagorean Theorem to find the side adjacent to point B (6). The tangent of angle CBA is thus the parallelogram’s height (8), over the newly found adjacent side (6), which simplifies to 4/3.
