TRIGONOMETRY BASICS

• The value of the original problem, cosecant negative thirteen pi over six, is negative two.
• Sine of some angle theta is equal to the opposite side divided by the hypotenuse.
• Cosine of some angle theta is equal to the adjacent side divided by the hypotenuse.
• Tangent ratio is equal to the opposite side divided by the adjacent side.
• SOHCAHTOA helps us to remember the formulas dealing with the three most common trig ratios: Sine, Cosine, and Tangent.
• SOHCAHTOA stands for Sine, Opposite, Hypotenuse, Cosine, and Tangent.
• In SOHCAHTOA, 'Sine' is represented by 'SO'.
• In SOHCAHTOA, 'Cosine' is represented by 'CA'.
• The secant ratio is the reciprocal of the cosine ratio, also known as the hyperbolic cosine.
• There are certain right triangles, known as special right triangles, that you should commit to memory, including the 3-4-5 right triangle, the 5-12-13 triangle, the 8-15-17 triangle, and the 7-24-25 right triangle.
• The tangent ratio is equal to the opposite side divided by the adjacent side.
• The cosecant ratio is the reciprocal of the sine ratio, also known as the hyperbolic sine.
• The sine, cosine, and tangent ratios can be calculated in a right triangle.
• The sine ratio is equal to the opposite side divided by the hypotenuse.
• The cotangent ratio is the reciprocal of the tangent ratio, also known as the hyperbolic tangent.
• The cosine ratio is equal to the adjacent side divided by the hypotenuse.
• The Pythagorean theorem can be used to find the missing side in a right triangle.
• In SOHCAHTOA, 'Tangent' is represented by 'TOA'.
• The hypotenuse of a right triangle is always positive.
• The 45 45 90 right triangle states that the side across the 45 angle is equal to one and the side across the 90 angle is the square root of two.
• To evaluate sine of 240 degrees, draw a reference angle and measure it traveling in a counterclockwise direction for positive angles and in a clockwise direction for negative angles.
• Tangent of pi over four or tangent of 45 degrees is one.
• The difference between the reference angle and the angle you are evaluating is known as the reference angle.
• Across the 90 degree angle, the side length is two.
• The three angles of a right triangle must always add up to 180 degrees.
• When dividing by four, you can half the number twice to get the same result as cosine of 45 degrees.
• Across the 60 degree angle in a 30 60 90 triangle, the side length is the square root of three.
• Across the 30 degree angle, the side length is one.
• The reference angle is the angle between the x-axis and your terminal ray, which is where your ray should stop.
• To evaluate sine of 240 degrees using a reference triangle, the opposite to the reference angle is negative square root 3 and the hypotenuse is 2.
• Cosine 45 is equal to the square root of two over two.
• The reference angle in quadrant four is 360 minus the angle in quadrant four.
• The cosine of 150 degrees, located in quadrant two, is negative square root 3 over 2.
• The sine of 240 degrees is negative square root 3 over 2, which can also be represented as negative 0.866.
• The reference angle in quadrant two is 30 degrees, which is the difference between the angle in quadrant two and 180 degrees.
• The reference angle in quadrant three is the difference between the angle in quadrant three and 180 degrees.
• The triangle in quadrant two is located on the negative x-axis, so the hypotenuse is negative square root 3.
• The triangle in quadrant two has a 30 degree angle, a side length of 1 across the 30 degree angle, and a hypotenuse of square root 3.
• The cosine of 30 degrees, which can be found on a calculator, is positive square root 3 over 2.
• The cosine of 5 pi over 6 is equal to cosine of 150 degrees, which is located in quadrant two.