Students usually have difficulty on the second part of question 3 on yesterday's quiz review. If students ask about it, I will choose a student who did get it correct and have them show their work. When writing cos(arcsin 1/4 + arccos 3/4) as an algebraic expression, students may not realize that arcsin(1/4) and arccos(3/4) are two separate angles. My students sometimes try to represent both of these angles by drawing one triangle and then getting confused when they realize that it is impossible for an angle to have a sine of 1/4 and a cosine of 3/4.
Other students don't see the need to use the cos(A + B) formula for this problem. Reminding them that arcsin(1/4) and arccos(3/4) represent angles will help to solidify this fact.
Here are some sample problems that you may choose to use for your quiz over this portion of the unit. More than anything, this formative assessment will give students practice with the formulas and will assess their progress. Typically, students will know the formulas well, but will forget a negative sign here or there.
For question 1, I will usually have a few students who have major misconceptions and will evaluate cos(-12/13) thinking that -12/13 is the angle measure. Other students may distribute the cosine to A and B to get cosA - cosB. This is a good time to intervene with these students so that they can get clarification before the unit assessment. I discuss this more in the video below.
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