Trigonometry (Virginia SOL)

Triangle Trigonometry (TT)

• T.TT.1 Use the six trigonometric ratios of acute angles in right triangles to solve real-world and geometric problems.
• Define and represent the six trigonometric ratios of an angle in a right triangle.
• Describe how side lengths relate in 30°-60°-90° and 45°-45°-90° triangles.
• Use trig functions, the Pythagorean theorem and the Laws of Sines and Cosines in problems in context.
• Model and solve right-triangle word problems, including angles of elevation and depression.
• T.TT.2 Find the area of any triangle and solve for missing sides and angles of non-right triangles with the Laws of Sines and Cosines.
• Apply the Laws of Sines and Cosines to find missing parts of non-right triangles.
• Recognize the ambiguous case of the Law of Sines and when two triangles are possible.
• Solve problems that combine both laws and the triangle area formula, including in context.

Circular Trigonometry (CT)

• T.CT.1 Measure angles in degrees and radians, sketch angles in standard position and find trig values from a point or a known value.
• Define a radian and relate radian measure to the length of the intercepted arc.
• Convert between degrees and radians for positive and negative rotations.
• Find positive and negative coterminal angles.
• Identify the quadrant or axis on which an angle's terminal side lies.
• Sketch a reference right triangle from a point on the terminal side.
• Sketch a reference right triangle from a given trig function value.
• Find any trig function value from a point on the terminal side.
• Find the other five trig function values from one known value.
• Calculate arc length using radians.
• Calculate the area of a sector of a circle.
• T.CT.2 Develop and use properties of the unit circle in degrees and radians, including values for special angles.
• Convert between degrees and radians for the special angles of the unit circle without technology.
• Define the six circular trig functions for an angle in standard position on the unit circle.
• Find trig values of special and related angles with right triangles and the unit circle, without technology.

Graphs of Trigonometric Functions (GT)

• T.GT.1 Graph and analyze trigonometric functions and use them to model periodic situations.
• Sketch the six parent trig functions over at least two periods.
• Find domain, range, amplitude, period and asymptotes from a graph or an equation.
• Use graphing technology to show how the parameters A, B, C and D change a graph.
• Sketch transformed sine, cosine and tangent graphs written in standard form over two periods.
• Use trig functions and their graphs to model periodic phenomena.
• T.GT.2 Graph the six inverse trigonometric functions.
• Find the domain and range of the inverse trig functions.
• Use domain restrictions to find values of inverse trig functions.
• Graph the inverse trig functions.

Identities and Equations (IE)

• T.IE.1 Evaluate expressions with the six trig functions and with inverse sine, cosine and tangent.
• Find trig function values with and without graphing technology.
• Find angle measures with inverse trig functions, with or without technology.
• Evaluate compositions of trig and inverse trig functions.
• T.IE.2 Use basic identity substitutions to simplify and verify trigonometric identities.
• Use reciprocal, Pythagorean, sum and difference, double-angle and half-angle identities to simplify and verify expressions.
• Use sum, difference and half-angle identities to find exact values for angles that are not special angles, including in context.
• T.IE.3 Solve trigonometric equations and inequalities algebraically and graphically and check solutions with technology.
• Solve trig equations on restricted and unrestricted domains algebraically and graphically.
• Solve trig inequalities algebraically and graphically.
• Check and justify solutions with graphing technology.