Montana Math MT.PLUS.ALG.TRIG.1

MT.PLUS.ALG.TRIG.1 is a cluster heading. These are the individual standards under it.

• MT.PLUS.ALG.TRIG.1.a

  Defining the sine and cosine functions in terms of the unit circle, and

• MT.PLUS.ALG.TRIG.1.b

  Defining the tangent, cotangent, secant, and cosecant functions in terms of sine and cosine.

01

What Students Need to Do

Students locate the point on a unit circle for any real angle, including negative angles and angles past one turn. They read cosine from the x-coordinate and sine from the y-coordinate, then use those values to find the other four trig functions when defined.

02

What Mastery Looks Like

Given 5π/4, a student finds the point (−√2/2, −√2/2) and calculates all six trig values. They explain why tangent and secant are undefined at π/2: cosine is zero.

03

Common Misconceptions

Students may swap the coordinates and call the x-coordinate sine. They may assume every negative angle lands in quadrant III or try to divide by zero to find tangent at π/2.

04

How to Assess It

Exit ticket: For 3π/2, give the unit-circle point and all six trig values. Mark any undefined values and explain one using a zero denominator.

1. 01

   Draw a unit circle on graph paper, use a protractor to mark positive and negative angles, and record each point's coordinates.

2. 02

   Ask: Why is tangent undefined at π/2 while sine is 1? Have students explain using the point (0, 1).

3. 03

   Play angle-card match: pair angle cards with coordinate cards, then calculate tangent, cotangent, secant, and cosecant from sine and cosine.

4. 04

   Draw a bicycle wheel as a unit circle, and predict a spoke tip's coordinates after a 5π/2 turn.

• MT.PLUS.ALG.TRIG.3

  Graph trigonometric functions with and without the use of technology by: Graphing sine and cosine functions, identifying period, midline, and amplitude, and Gra...

• MT.CORE.GEOM.MEAS.3

  Use similarity to explore and define the sine ratio, cosine ratio, and tangent ratio in terms of right triangles by: Deriving and applying the trigonometric rat...