Round to four decimal places. An airplane has only enough gas to fly to a city miles northeast of its current location. If the pilot knows that the city is 25 miles north, how many degrees north of east should the airplane fly?
If a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 15 feet long, what angle does the ramp make with the ground? If a loading ramp is placed next to a truck, at a height of 2 feet, and the ramp is 20 feet long, what angle does the ramp make with the ground?
A woman is watching a launched rocket currently 11 miles in altitude. If she is standing 4 miles from the launch pad, at what angle is she looking up from horizontal?
An astronaut is in a launched rocket currently 15 miles in altitude. If a man is standing 2 miles from the launch pad, at what angle is she looking down at him from horizontal? Hint: this is called the angle of depression. A woman is standing 8 meters away from a meter tall building. At what angle is she looking to the top of the building? A man is standing 10 meters away from a 6-meter tall building.
Someone at the top of the building is looking down at him. At what angle is the person looking at him? A foot tall building has a shadow that is 55 feet long. What is the angle of elevation of the sun? A foot tall building has a shadow that is 2 feet long. A spotlight on the ground 3 meters from a 2-meter tall man casts a 6 meter shadow on a wall 6 meters from the man. At what angle is the light? A spotlight on the ground 3 feet from a 5-foot tall woman casts a foot tall shadow on a wall 6 feet from the woman.
For the following exercises, find a solution to the following word problem algebraically. Then use a calculator to verify the result. Round the answer to the nearest tenth of a degree.
A person does a handstand with his feet touching a wall and his hands 1. If the person is 6 feet tall, what angle do his feet make with the wall? A person does a handstand with her feet touching a wall and her hands 3 feet away from the wall.
If the person is 5 feet tall, what angle do her feet make with the wall? A foot ladder is positioned next to a house. If the ladder slips at 7 feet from the house when there is not enough traction, what angle should the ladder make with the ground to avoid slipping? Skip to main content. Module 3: Trigonometric Identities and Equations. Search for:. Solving Trigonometric Equations Solving Linear Trigonometric Equations in Sine and Cosine Trigonometric equations are, as the name implies, equations that involve trigonometric functions.
How To: Given a trigonometric equation, solve using algebra. Look for a pattern that suggests an algebraic property, such as the difference of squares or a factoring opportunity.
Solve the equation the same way an algebraic equation would be solved. Substitute the trigonometric expression back in for the variable in the resulting expressions. Solve for the angle. Solution Use algebraic techniques to solve the equation.
Solution Make sure mode is set to radians. Analysis of the Solution Note that a calculator will only return an angle in quadrants I or IV for the sine function, since that is the range of the inverse sine. Solution We can begin with some algebra. Figure 2. Solution As this problem is not easily factored, we will solve using the square root property. Solution We can solve this equation using only algebra. Solution Using grouping, this quadratic can be factored.
Analysis of the Solution Make sure to check all solutions on the given domain as some factors have no solution. Solution This problem should appear familiar as it is similar to a quadratic. Sine, Cosine, and Tangent are the three basic functions of trigonometry through which trigonometric identities, trigonometry functions, and formulas are formed.
The tangent is defined as the ratio of the length of the opposite side or perpendicular of a right angle to the angle and the length of the adjacent side. Tangent function in trigonometry is used to calculate the slope of a line between the origin and a point defining the intersection between hypotenuse and altitude of a right-angle triangle. In this article, we will discuss the tan 0 values and how to derive the tan 0 degrees value. The Value of Tan 0 degrees equal to zero.
Graphing Cosine Function The trigonometric ratios can also be considered as functions of a variable which is the measure of an angle. Subjects Near Me. Download our free learning tools apps and test prep books. Varsity Tutors does not have affiliation with universities mentioned on its website.
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