Finding the value of trigonometric functions for specific angles is a skill that is developed over time. As with all things math, practice makes perfect!
Trigonometry refers to the study of triangles and the ratios of their sides. There are three types of trigonometry: spherical, planar, and linear. Spherical trigonometry deals with the ratios of sides on a sphere, planar trigonometry deals with plane angles, and linear trigonometry deals with straight lines.
When finding the value of a specific angle’s cosine or sine, the length of the side opposite that angle is constant. This makes it easy to find the ratio of the cosine or sine for that specific angle.
In this blog post, we will discuss how to find the value of an angle’s cosine with regard to an angle whose terminating side terminates at (x,-y)2.
Use the angle formula with θ
The cosine of an angle is a value that represents the size and direction of the triangle created by the angle.
The cosine of an angle is a ratio that expresses the length of the side adjacent to the angle divided by the length of the side terminating at the angle point.
How to find Cosine? The cosine can be found using the following formula: Cos A = B / A Where A = Length of Adjacent Side, B = Length of Terminating Side
As we can see, this formula requires you to know two sides of a triangle: one side adjacent to the given angle and one side terminating at the given angle point. You must also know these sides’ lengths.
You can also find cosine using geometry software or apps. These programs will ask you for an angle and give you back its cosine, or you can enter two sides of a triangle and it will give you back all three values.
Use the triangle opposite angle θ
Next, we use the triangle opposite angle θ to find the cosine of angle θ. We already have one side of this new triangle, which is the length of side a.
We will use a very special triangle called a Pythagorean triple. It has sides that are ratios of whole numbers. A common one is a 3-4-5 triangle, where side a is 3 and b is 4, so that the ratio of these two sides is 1:2.
We will use this to find the cosine of angle θ by finding another side using the adjacent side (a) and the hypotenuse (b) of a 3-4-5 triangle with side a = 1. We will then take cosine(θ) = b / 1 = 2, so we can plug this into our original equation.
Calculate cosine of θ using a calculator
To calculate the cosine of an angle using a calculator, first enter the angle in degrees as a value, then enter 1 as the cosine value, and finally, press the cos or sin button, depending on your calculator.
Many calculators have a quadrant function that allows you to enter an angle in one quadrant and it will display the angle in the other quadrants. For example, if you enter an angle of 45° in the northwest (1st) quadrant and press “cos” or “sin” it will give you -1 as the cosine value.
This is useful because it helps you know if an angle is facing north or south by seeing which number is negative. By knowing this information, you can determine which side of the point (16, −30) an angle with terminating sides ends on.
Find the terminating side and use its opposite angle to find cosine of θ
The first step in this problem is to find the terminating side of the angle θ. In this case, it is the side opposite of point (16, −30) on the triangle.
The second step is to use the cosine function with angle θ’s opposite side length and 1 as the arguments. This makes sense because if cosine of θ = a / b then b = cosθ × a so b = 1 and a = θ’s opposite side length.
Therefore, the value of cosine is b / 1 which simplifies to b so the answer is B.
This problem can be tricky if you do not notice that the given information is for an angle with its terminating side, not an angle that terminates at that given point.
Use trigonometric identity to find cosine of Θ| style=”text-align:center;” |>| style=”text-align:center;” |>| style=”text-align:center;” |>| style=”text-align:center;” |>| style=”text-align:center;” |>| style=”text-align:center;” |>|}
Another way to find the cosine of an angle with its terminating side on a given point is to use the inverse cosine identity.
The inverse cosine identity states that if acos(A−B) = 1, then A=B. What this means is that you can find the angle A by rotating B degrees, so they are equivalent angles.
To use this identity, first find the length of the side of the triangle formed by the given point (in this case, (16, −30) and (18, −32)) using basic geometry principles. Then find the length of one of the sides using basic geometry principles.
