Q: Is sohcahtoa only for right triangles? A: **Yes, it only applies to right triangles**. If we have an oblique triangle, then we can't assume these trig ratios will work. We have other methods we'll learn about in Math Analysis and Trigonometry such as the laws of sines and cosines to handle those cases.

**Overview**

- Put the equation in terms of one function of one angle.
- Write the equation as one trig function of an angle equals a constant.
- Write down the possible value(s) for the angle.
- If necessary, solve for the variable.
- Apply any restrictions on the solution.

**5 strategies you can use to solve TRIG IDENTITIES**

- See what you can FACTOR. Sometimes, factoring with a common term will make everything into a trig identity.
- Multiply the denominator by a CONJUGATE.
- Get a COMMON DENOMINATOR.
- SPLIT UP A FRACTION into two separate fractions.
- Rewrite everything in terms of SINE AND COSINE.

Simplify left side using the identity cos(arccos(A)) = A. Expand the right side using the identity cos(a + b) = cos(a). cos(b) - sin(a)sin(b). Use cos(π / 2) = 0 , sin( arcsin(x)) = x and sin(π / 2) = 1 to simplify the right side of the equation.

The following are some tips which will serve you well. * **Revise the domain, range and graphs of all of the trigonometric and inverse trigonometric functions**. * Make sure you understand the difference between the trigonometric and inverse trigonometric functions. Finally, practise, practise and practise.

The most commonly used acronym to remember these ratios is SOHCAHTOA, which stands for "Sine Opposite Hypotenuse, Cosine Adjacent Hypotenuse, Tangent Opposite Adjacent." You can better remember this acronym by **spelling out a mnemonic phrase with these letters**.

Q: Is sohcahtoa only for right triangles? A: **Yes, it only applies to right triangles**. If we have an oblique triangle, then we can't assume these trig ratios will work. We have other methods we'll learn about in Math Analysis and Trigonometry such as the laws of sines and cosines to handle those cases.

In general, trigonometry is taken as part of **sophomore or junior year math**. In addition to being offered as its own course, trigonometry is often incorporated as a unit or semester focus in other math courses.

Consider, the function y = f(x), and x = g(y) then the inverse function is written as **g = f ^{-}^{1}**, This means that if y=f(x), then x = f

**Overview**

- Put the equation in terms of one function of one angle.
- Write the equation as one trig function of an angle equals a constant.
- Write down the possible value(s) for the angle.
- If necessary, solve for the variable.
- Apply any restrictions on the solution.

In a right-angled triangle, the cosine of an angle (θ) is the ratio of its adjacent side to the hypotenuse, that is, cos θ = (adjacent side) / (hypotenuse). Using the definition of inverse cosine, **θ = cos ^{-}^{1}**.

The sine, cosine, and tangent ratios in a right triangle can be remembered by representing them as strings of letters, for instance **SOH-CAH-TOA** in English: Sine = Opposite ÷ Hypotenuse. Cosine = Adjacent ÷ Hypotenuse. Tangent = Opposite ÷ Adjacent.

To memorize the unit circle, **use the acronym ASAP, which stands for "All, Subtract, Add, Prime."** Each word represents a different quadrant in the unit circle. "All" corresponds with the top right quadrant in the circle, or the first quadrant.

Cos inverse x can also be written as **arccos x**. If y = cos x ⇒ x = cos^{-}^{1}(y). Let us consider a few examples to see how the inverse cosine function works. In a right-angled triangle, the cosine of an angle (θ) is the ratio of its adjacent side to the hypotenuse, that is, cos θ = (adjacent side) / (hypotenuse).

**The arcsin function is the inverse of the sine function**. It returns the angle whose sine is a given number.

arcsin.

sin30 = 0.5 | Means: The sine of 30 degrees is 0.5 |
---|---|

arcsin 0.5 = 30 | Means: The angle whose sin is 0.5 is 30 degrees. |

Try this Drag any vertex of the triangle and see how the angle C is calculated using the arccos() function. Means: The angle whose cosine is 0.866 is 30 degrees. Use arccos when you know the cosine of an angle and want to know the actual angle.

For y = arccos x :

Range | 0 ≤ y ≤ π 0 ° ≤ y ≤ 180 ° |
---|---|

Domain | − 1 ≤ x ≤ 1 |

**Inverse Sine Function**

- Start with:sin a° = opposite/hypotenuse.
- sin a° = 18.88/30.
- Calculate 18.88/30:sin a° = 0.6293
- Inverse Sine:a° = sin
^{−}^{1}(0.6293) - Use a calculator to find sin
^{−}^{1}(0.6293 ):a° = 39.0° (to 1 decimal place)

Remember, **if the angles of a triangle remain the same, but the sides increase or decrease in length proportionally, these ratios remain the same**. Therefore, trigonometric ratios in right triangles are dependent only on the size of the angles, not on the lengths of the sides.

**When answering a trigonometry problem:**

- label the sides on the triangle.
- decide which ratio to use (SOH CAH TOA)
- substitute the correct information into the ratio.
- rearrange to find ' '
- solve using your calculator making sure your calculator is set to 'degrees' mode.

There are three basic functions in trigonometry, each of which is one side of a right-angled triangle divided by another. You may find it helpful to remember **Sine, Cosine and Tangent** as SOH CAH TOA. Remembering trigonometric functions can be difficult and confusing to begin with. Even SOH CAH TOA can be tricky.

You could learn the basic ideas fairly quickly, like in **a few days**.. but it would be much better if you learned to use the tools for problems so you understand how they relate. 'This takes time, you need a bit of patience, I think a few months would be a good target with 30min-1h work every day.

Dated : 01-Jun-2022

Category : Education