find the following trigonometric values.
express your answers exactly.

$\cos(315^{\circ}) = $

$\sin(315^{\circ}) = $

Question

find the following trigonometric values.
express your answers exactly.

$\cos(315^{\circ}) = $

$\sin(315^{\circ}) = $

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Trigonometric Reference Angles", "Unit Circle Values" ], "current_concepts": [ "Trigonometric Reference Angles", "Unit Circle Values" ] } ## Find the reference angle $$ \theta' = 360^\circ - 315^\circ = 45^\circ $$ ## Determine the quadrant and signs $$ \begin{aligned} &315^\circ \in \text{Quadrant IV} \ &\cos(315^\circ) > 0 \ &\sin(315^\circ) < 0 \end{aligned} $$ ## Calculate exact values $$ \begin{aligned} &\cos(315^\circ) = \cos(45^\circ) = \frac{\sqrt{2}}{2} \ &\sin(315^\circ) = -\sin(45^\circ) = -\frac{\sqrt{2}}{2} \end{aligned} $$ ## Question 1 $\cos(315^\circ) =$ $\frac{\sqrt{2}}{2}$ ## Question 2 $\sin(315^\circ) =$ -$\frac{\sqrt{2}}{2}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Trigonometric Reference Angles" ] }

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QUESTION IMAGE

Question

Explanation:

Find the reference angle

Determine the quadrant and signs

Calculate exact values

Answer:

Question 1

Question 2