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Which pair of angles has congruent values for the [tex]\sin x^{\circ}[/tex] and the [tex]\cos y^{\circ}[/tex]?

A. [tex]70^{\circ} ; 160^{\circ}[/tex]
B. [tex]70^{\circ} ; 70^{\circ}[/tex]
C. [tex]70^{\circ} ; 120^{\circ}[/tex]
D. [tex]70^{\circ} ; 20^{\circ}[/tex]

Sagot :

GinnyAnsweridn
To determine which pair of angles has congruent values for [tex]\(\sin x^{\circ}\)[/tex] and [tex]\(\cos y^{\circ}\)[/tex], let's evaluate each pair individually.

1. Pair: [tex]\(70^{\circ}\)[/tex] and [tex]\(160^{\circ}\)[/tex]
- [tex]\(\sin(70^{\circ}) \approx 0.9397\)[/tex]
- [tex]\(\cos(160^{\circ}) \approx -0.9397\)[/tex]

2. Pair: [tex]\(70^{\circ}\)[/tex] and [tex]\(70^{\circ}\)[/tex]
- [tex]\(\sin(70^{\circ}) \approx 0.9397\)[/tex]
- [tex]\(\cos(70^{\circ}) \approx 0.3420\)[/tex]

3. Pair: [tex]\(70^{\circ}\)[/tex] and [tex]\(120^{\circ}\)[/tex]
- [tex]\(\sin(70^{\circ}) \approx 0.9397\)[/tex]
- [tex]\(\cos(120^{\circ}) \approx -0.5000\)[/tex]

4. Pair: [tex]\(70^{\circ}\)[/tex] and [tex]\(20^{\circ}\)[/tex]
- [tex]\(\sin(70^{\circ}) \approx 0.9397\)[/tex]
- [tex]\(\cos(20^{\circ}) \approx 0.9397\)[/tex]

Therefore, the pair of angles that have congruent values for [tex]\(\sin x^{\circ}\)[/tex] and [tex]\(\cos y^{\circ}\)[/tex] is the pair [tex]\(70^{\circ}\)[/tex] and [tex]\(20^{\circ}\)[/tex].
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