Question

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.
match each sine or cosine value to its equivalent measure.
cos(58°) cos(137°) sin(16°) sin(123°) sin(33°) cos(47°)
sin(106°)
cos(57°)
cos(74°)
sin(43°)
sin(32°)
reset next

Explanation:

We use the co - function identities \(\sin\theta=\cos(90^{\circ}-\theta)\) and \(\cos\theta=\sin(90^{\circ}-\theta)\), and also the supplementary angle identities \(\sin(180^{\circ}-\alpha)=\sin\alpha\) and \(\cos(180^{\circ}-\alpha)=-\cos\alpha\) (but we focus on the positive equivalent in terms of angle measure for the matching here).

Step 1: Match \(\cos(57^{\circ})\)

We know that \(\cos\theta=\sin(90^{\circ}-\theta)\). So, \(90 - 57=33\). So \(\cos(57^{\circ})=\sin(33^{\circ})\)

Step 2: Match \(\cos(74^{\circ})\)

Using \(\cos\theta=\sin(90^{\circ}-\theta)\), \(90 - 74 = 16\). So \(\cos(74^{\circ})=\sin(16^{\circ})\)

Step 3: Match \(\sin(43^{\circ})\)

Using \(\sin\theta=\cos(90^{\circ}-\theta)\), \(90 - 43=47\). So \(\sin(43^{\circ})=\cos(47^{\circ})\)

Step 4: Match \(\sin(32^{\circ})\)

Using \(\sin\theta=\cos(90^{\circ}-\theta)\), \(90 - 32 = 58\). So \(\sin(32^{\circ})=\cos(58^{\circ})\)

Also, for the other angles:

• \(\sin(106^{\circ})=\sin(180 - 74)^{\circ}=\sin(74^{\circ})\) but we already used the main four matches above. And \(\sin(123^{\circ})=\sin(180 - 57)^{\circ}=\sin(57^{\circ})\), \(\cos(137^{\circ})=\cos(180 - 43)^{\circ}=-\cos(43^{\circ})\) (not used in the given matches as we are looking for positive equivalent angle measure for the given tiles)

Answer:

• \(\cos(57^{\circ})\) \(\longleftrightarrow\) \(\sin(33^{\circ})\)
• \(\cos(74^{\circ})\) \(\longleftrightarrow\) \(\sin(16^{\circ})\)
• \(\sin(43^{\circ})\) \(\longleftrightarrow\) \(\cos(47^{\circ})\)
• \(\sin(32^{\circ})\) \(\longleftrightarrow\) \(\cos(58^{\circ})\)