- #1
Nexus555
- 58
- 0
Homework Statement
4sec180° - 2sin2270°
The Attempt at a Solution
sec(180 is -1.
So we have 4(-1) which is -4
sin2(270 is -1
So we have 2(-1)
This now reads -4 - -2
Answer = -2
Is this correct or do I suck at this? =(
Secant (sec), sine (sin), and cosine (cos) are trigonometric functions used to calculate the ratios of sides in a right triangle. Secant is the reciprocal of cosine, and sine is the reciprocal of cosine. Cosine represents the adjacent side over the hypotenuse, while sine represents the opposite side over the hypotenuse.
These trigonometric functions are used in various fields, including engineering, physics, and navigation. For example, secant and tangent can be used to calculate the height of a building or the length of a shadow. Sine and cosine are used in analyzing wave patterns in physics and in determining ship and aircraft positions in navigation.
The unit circle is a circle with a radius of 1 centered at the origin of a coordinate system. It is used to understand the values of trigonometric functions at different angles. The x-coordinate of a point on the unit circle represents cosine, and the y-coordinate represents sine. Therefore, secant and tangent can be calculated by taking the reciprocal of cosine and sine, respectively.
One way to remember the values of these trigonometric functions is through the acronym "SOHCAHTOA", which stands for "sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent". You can also create a table or use a calculator to determine the values for specific angles.
One common mistake is confusing the inverse trigonometric functions, such as secant, cosecant, and cotangent, with the reciprocal functions, such as secant, sine, and cosine. Another mistake is forgetting to convert between degrees and radians when necessary. It is also important to pay attention to the signs of the values, as they can change depending on the quadrant of the angle.