- 4-7.R.0: Update your journal with what you have learned in this chapter. Inc...
- 4-7.R.1: Figure 4-7a shows a unit circle and an angle in standard position. ...
- 4-7.R.2: a. Write equations expressing tan x and cot x in terms of sin x and...
- 4-7.R.3: a. Transform tan A sin A + cos A to sec A. What values of A are exc...
- 4-7.R.4: a. Find the general solution for = arcsin 0. b. Solve 1 + tan 2 (x ...
- 4-7.R.5: a. Plot the graph of this parametric function on your grapher. Sket...
- 4-7.R.6: a. Using parametric mode on your grapher, duplicate the graph of th...
- 4-7.C.1: Pendulum Problem: Figure 4-7d shows a pendulum hanging from the cei...
- 4-7.C.2: Prove that each of these equations is an identity. a. b. C
- 4-7.C.3: Square of a Sinusoid Problem: Figure 4-7e shows the graphs of y1 = ...
- 4-7.T.1: Write the Pythagorean property for cosine and sine. T
- 4-7.T.2: Write a quotient property involving cosine and sine. T
- 4-7.T.3: Write the reciprocal property for cotangent. T
- 4-7.T.4: Write the reciprocal property for secant. T
- 4-7.T.5: The value of sin1 0.5 is 30. Write the general solution for = arcsi...
- 4-7.T.6: The value of tan1 is . Write the general solution for x = arctan . T
- 4-7.T.7: Explain why the range of y = cos1 x is [0, ] but the range of y = s...
- 4-7.T.8: Find geometrically the exact value of cos (tan1 2). T
- 4-7.T.9: Transform (1 + sin A)(1 sin A) to cos2 A. What values of A are excl...
- 4-7.T.10: Prove that tan B + cot B = csc B sec B is an identity. What values ...
- 4-7.T.11: Multiply the numerator and denominator of by the conjugate of the d...
- 4-7.T.12: Plot the graphs of both expressions in T11 to confirm that the two ...
- 4-7.T.13: With your calculator in degree mode, find the value of cos1 0. Show...
- 4-7.T.14: Find another angle between 0 and 360 whose cosine is 0. Show it on ...
- 4-7.T.15: Write the general solution for the inverse trigonometric relation =...
- 4-7.T.16: Find the fifth positive value of for which cos = 0. How many revolu...
- 4-7.T.17: Find algebraically the general solution for 4 tan ( 25) = 7 T1
- 4-7.T.18: Write parametric equations for this ellipse (Figure 4-7f). Figure 4...
- 4-7.T.19: Write the parametric equations you use to plot y = arctan x (Figure...
- 4-7.T.20: What did you learn as a result of working this test that you did no...
Solutions for Chapter 4-7: Trigonometric Function Properties, Identities, and Parametric Functions
Full solutions for Precalculus with Trigonometry: Concepts and Applications | 1st Edition
Solutions for Chapter 4-7: Trigonometric Function Properties, Identities, and Parametric FunctionsGet Full Solutions
A letter or symbol that stands for a specific number,
A function that is continuous on its entire domain
A ratio equal to 1, used for unit conversion
Unit of measurement (represented by the symbol ) for angles or arcs, equal to 1/360 of a complete revolution
Domain of a function
The set of all input values for a function
An identity involving a trigonometric function of 2u
See Ellipse, Hyperbola, Parabola.
Inverse composition rule
The composition of a one-toone function with its inverse results in the identity function.
Logarithmic re-expression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression
Length of 1 minute of arc along the Earth’s equator.
Reciprocal of a real number
See Multiplicative inverse of a real number.
Reflection through the origin
x, y and (-x,-y) are reflections of each other through the origin.
Resolving a vector
Finding the horizontal and vertical components of a vector.
A number that measures a quantitative variable for a sample from a population.
Sum of a finite geometric series
Sn = a111 - r n 2 1 - r
Sum of two vectors
<u1, u2> + <v1, v2> = <u1 + v1, u2 + v2> <u1 + v1, u2 + v2, u3 + v3>
A circle with radius 1 centered at the origin.
Vertex of a parabola
The point of intersection of a parabola and its line of symmetry.
The directed distance from the xy-plane to a point in space, or the third number in an ordered triple.